Multi-factor coupling error compensation calibration method for external water pressure test of gas cylinder

Abstract

The application discloses a multi-factor coupling error compensation calibration method for gas cylinder external water pressure test, and relates to the technical field of special equipment.The application couples and weights each systematic error value, the corresponding error effectiveness coefficient and the preset weight coefficient to generate a high-precision compensated standard bottle calibration deformation, and uses the same as the final calibration value of the standard bottle to calibrate the water pressure test device, simultaneously updates the calibration parameter library to form a closed-loop feedback.In general, the application adopts a three-in-one technical path of multi-factor decoupling, dynamic reliability evaluation and adaptive weighted compensation, greatly improves the accuracy, stability and repeatability of the standard bottle calibration result, fundamentally enhances the overall reliability and intelligent level of the gas cylinder water pressure test system, and provides solid technical support for the safety inspection of special equipment.

Description

Technical Field

[0001] This invention relates to the field of special equipment technology, and in particular to a multi-factor coupling error compensation calibration method for external hydrostatic testing of gas cylinders. Background Technology

[0002] The external hydrostatic test of gas cylinders is a crucial step in the periodic inspection of special equipment, used to assess the structural integrity and safety performance of gas cylinders under high-pressure conditions. This method involves injecting high-pressure water into the cylinder and measuring its volumetric expansion to determine the presence of defects such as cracks, corrosion, or insufficient strength. To ensure the accuracy and comparability of the test results, the hydrostatic testing device must be calibrated using a "standard cylinder" with known precise deformation. The calibration accuracy of the standard cylinder directly determines the reliability of the entire testing system; therefore, the scientific validity and stability of its calibration method are paramount.

[0003] In practice, the "known precise deformation" of the standard bottle is not absolutely constant, but is affected by a variety of dynamic factors. First, pressure sensors exhibit nonlinearity and temperature drift characteristics, causing deviations between their output signals and the actual pressure in different operating ranges. Without localized fine compensation, this directly affects the accuracy of deformation calculation. Second, changes in ambient temperature simultaneously alter the bulk modulus of water and the thermal expansion state of the standard bottle material. The coupling effect of these two factors makes it difficult to accurately describe the equivalent volume shift using a single temperature compensation model. Furthermore, subjective differences among operators in controlling the water injection rate and determining the pressure stabilization time introduce additional dynamic disturbances, further contaminating the calibration data.

[0004] More importantly, existing calibration methods generally employ fixed error models and static weighting strategies, which directly superimpose compensation after assigning preset weights to various error terms. This method implicitly assumes that all error values ​​are within a reasonable and reliable range, lacking a dynamic evaluation mechanism for the reliability of the current error value itself. When an error significantly deviates from its normal distribution due to sudden interference (such as instantaneous sensor failure, environmental changes, or operational errors), its original value is still used for compensation, which can easily lead to distorted calibration results and even systemic misjudgments. Although some systems attempt to introduce threshold truncation (such as discarding values ​​exceeding ±2σ), this "hard truncation" method ignores the potential value of marginal data and cannot achieve continuous quantification of error reliability.

[0005] Therefore, there is an urgent need for a multi-factor coupling error compensation calibration method for external hydrostatic testing of gas cylinders. Summary of the Invention

[0006] To address the aforementioned technical problems, this invention provides a multi-factor coupling error compensation calibration method for external hydrostatic testing of gas cylinders, specifically comprising the following steps:

[0007] Step 1: Install the standard bottle into the water pressure testing device and simultaneously collect the pressure sensor output signal, ambient temperature data, water injection flow signal, and pressure fluctuation sequence during the pressure stabilization phase.

[0008] Step 2: Based on the pressure sensor output signal, ambient temperature data, water injection flow signal, and pressure fluctuation sequence during the pressure stabilization phase, obtain three systematic error values ​​that affect the calibration accuracy. These three systematic error values ​​include: the nonlinear drift of the pressure sensor within the current operating range, the equivalent volume offset caused by temperature changes, and the deformation correction term introduced by human operation.

[0009] Step 211: Determine the real-time pressure value during the current calibration process based on the pressure sensor output signal;

[0010] Step 212: Call the historical calibration database. The historical calibration database stores at least two sets of calibration records. Each set of calibration records contains a known standard pressure value and the pressure sensor output signal corresponding to the known standard pressure value.

[0011] Step 213: Based on at least two sets of calibration records in the historical calibration database, divide the measurement range of the pressure sensor into at least two continuous sub-intervals, and associate the endpoints of each sub-interval with a set of known standard pressure values ​​and the pressure sensor output signal corresponding to the known standard pressure values.

[0012] Step 214: When the real-time pressure value falls into any sub-interval, extract the pressure sensor output signal under the same known standard pressure value in the three most recent historical calibration databases within the current sub-interval, and calculate the average value. At the same time, combine the current pressure sensor output signal and solve the theoretical pressure value through a joint algorithm of local linear interpolation and least squares fitting. Use the difference between the theoretical pressure value and the real-time pressure value as the nonlinear drift of the pressure sensor in the current working interval.

[0013] Step 221: Based on the ambient temperature data, query the pre-stored functional relationship between the bulk elastic modulus of water and temperature, and calculate the volume compressibility coefficient of water at the current temperature;

[0014] Step 222: Obtain the reference volume, thermal expansion coefficient of the material, and preset reference temperature of the standard bottle, and calculate the change in thermal expansion volume of the standard bottle due to the deviation of the ambient temperature from the preset reference temperature based on the ambient temperature data, preset reference temperature, thermal expansion coefficient of the material, and reference volume.

[0015] Step 223: Algebraically superimpose the volume compression effect of water with the thermal expansion volume change of the standard bottle to obtain the equivalent volume shift caused by temperature change;

[0016] Step 231: Calculate the rate of change of water injection rate during the pressurization stage based on the water injection flow signal;

[0017] Step 232: Determine the actual stabilization time required from the end of pressurization to the stabilization of pressure fluctuations based on the pressure fluctuation sequence during the stabilization phase;

[0018] Step 233: Input the water injection rate change rate and the actual pressure stabilization time as input parameters into the pre-trained human factor operation bias model, and output the deformation correction term introduced by human operation;

[0019] Step 3: Perform validity analysis on each systematic error value, and obtain the error validity coefficient for each systematic error value based on the analysis results;

[0020] Step 31: Retrieve the historical error distribution dataset for each systematic error value;

[0021] Step 32: Based on the historical error distribution dataset, determine a reasonable threshold range for each systematic error value, wherein the reasonable threshold range includes a lower limit and an upper limit.

[0022] Step 33: Compare each of the currently acquired systematic error values ​​with the lower limit and upper limit of the reasonable threshold range for each systematic error value;

[0023] Step 34: If the current systematic error value is within the reasonable threshold range, calculate the first error validity coefficient of the current systematic error value based on the reasonable threshold range;

[0024] Step 341: Extract the lower and upper limits of the reasonable threshold range for the current systematic error value;

[0025] Step 342: Based on the lower limit and upper limit of the reasonable threshold range of the current systematic error value, calculate the middle threshold and width parameter of the reasonable threshold range, wherein the middle threshold is the arithmetic mean of the lower limit and the upper limit, and the width parameter is the difference between the upper limit and the lower limit.

[0026] Step 343: Calculate the absolute deviation between the current systematic error value and the intermediate threshold;

[0027] Step 344: Normalize the absolute deviation to obtain the normalized absolute deviation, which is the ratio of the absolute deviation to the width parameter.

[0028] Step 345: Using the absolute deviation and the width parameter as input variables, substitute them into the preset interval validity function to calculate the first error validity coefficient of the current systematic error value;

[0029] Step 35: If the current systematic error value is less than the lower limit of the reasonable threshold range, then calculate the second error effectiveness coefficient of the current systematic error value based on the reasonable threshold range and the first preset attenuation rule;

[0030] Step 351: Extract the lower limit and width parameters of the reasonable threshold range for the current systematic error value;

[0031] Step 352: Calculate the negative deviation between the current systematic error value and the lower limit value, wherein the negative deviation is the lower limit value minus the current systematic error value;

[0032] Step 353: Normalize the negative deviation to obtain a normalized negative deviation, wherein the normalized negative deviation is the ratio of the negative deviation to the width parameter.

[0033] Step 354: Substitute the normalized negative deviation into the first preset attenuation rule, where the first preset attenuation rule is a preset first attenuation function, and calculate the second error effectiveness coefficient.

[0034] Step 36: If the current systematic error value is greater than the upper limit of the reasonable threshold range, calculate the third error effectiveness coefficient of the current systematic error value based on the reasonable threshold range and the second preset attenuation rule;

[0035] Step 361: Extract the upper limit and width parameters of the reasonable threshold range for the current systematic error value;

[0036] Step 362: Calculate the positive deviation between the current systematic error value and the upper limit value, wherein the positive deviation is the current systematic error value minus the upper limit value;

[0037] Step 363: Normalize the positive deviation to obtain a normalized positive deviation, wherein the normalized positive deviation is the ratio of the positive deviation to the width parameter;

[0038] Step 364: Substitute the normalized positive deviation into the preset second decay function to calculate the third error effectiveness coefficient;

[0039] Step 4: Based on each systematic error value, the error effectiveness coefficient of each systematic error value, and the preset weighting coefficient of each systematic error value, obtain the compensated standard bottle calibration deformation amount;

[0040] Step 5: Use the compensated standard bottle's calibrated deformation as the final calibration value of the standard bottle, use the final calibration value of the standard bottle to calibrate the hydrostatic testing device, and update the calibration parameter library of the hydrostatic testing device simultaneously.

[0041] The embodiments of the present invention have the following technical effects:

[0042] This invention effectively separates and quantifies three key systematic error values ​​affecting the calibration accuracy of standard bottles by systematically integrating multi-source real-time sensor information, including pressure sensor output signals, ambient temperature data, water injection flow signals, and pressure fluctuation sequences during the pressure stabilization phase. These errors are: nonlinear drift of the pressure sensor within the current operating range, equivalent volume offset caused by temperature changes, and deformation correction terms introduced by human operation. Building upon this, the invention innovatively introduces a validity determination analysis mechanism based on historical error distribution datasets. For each systematic error value, its error validity coefficient is dynamically calculated. When the error value is within a reasonable threshold range, a first error validity coefficient is constructed using the normalized absolute deviation and the interval width parameter. When the error value is below the lower limit or above the upper limit, a second or third error validity coefficient is calculated based on the normalized negative or positive deviation, combined with a preset first or second attenuation function, respectively. This mechanism abandons the traditional "all or nothing" hard truncation strategy, achieving gradual attenuation utilization of marginal reliable data, significantly improving the robustness and adaptability of error compensation. Furthermore, this invention couples and weights various systematic error values ​​with their corresponding error effectiveness coefficients and preset weighting coefficients to generate a high-precision compensated standard bottle calibration deformation. This deformation is then used as the final calibration value of the standard bottle for calibrating the hydrostatic testing device, while simultaneously updating the calibration parameter library to form a closed-loop feedback. This not only solves the calibration deviation problem caused by the lack of fine modeling of local nonlinearity in the sensors, but also overcomes the insufficient temperature change compensation caused by the coupling of water compressibility and the thermal expansion effect of the standard bottle. It also quantifies and suppresses the uncertainty of human operation characterized by the rate of change of water injection rate and the actual pressure stabilization time. Overall, this invention, through a three-pronged technical approach of multi-factor decoupling, dynamic reliability assessment, and adaptive weighted compensation, significantly improves the accuracy, stability, and repeatability of the standard bottle calibration results, thereby fundamentally enhancing the overall reliability and intelligence level of the gas cylinder hydrostatic testing system and providing solid technical support for the safety inspection of special equipment. Attached Figure Description

[0043] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0044] Figure 1 This is a flowchart of a multi-factor coupling error compensation calibration method for external hydrostatic testing of gas cylinders, provided in an embodiment of the present invention. Detailed Implementation

[0045] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below. Obviously, the described embodiments are only a part of the embodiments of this invention, and not all of them. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this invention.

[0046] Example 1: As Figure 1 As shown, the present invention provides a multi-factor coupling error compensation calibration method for external hydrostatic testing of gas cylinders, comprising the following steps:

[0047] Step 1: Install the standard bottle into the water pressure testing device and simultaneously collect the pressure sensor output signal, ambient temperature data, water injection flow signal, and pressure fluctuation sequence during the pressure stabilization phase.

[0048] It is worth noting that when performing step 1, the standard bottle should first be securely installed in the test position of the water pressure testing device to ensure that it is fully connected with the high-pressure water injection circuit, pressure sensing interface and sealing fixture, and there is no risk of leakage. After installation, the data acquisition module of the hydrostatic test system is activated, and the multi-channel sensors are simultaneously triggered to work together. The pressure sensor output signal is acquired in real time by a high-precision pressure transmitter installed at the inlet of the standard bottle or on the main circuit of the system, with a sampling frequency of no less than 100 Hz to fully capture the dynamic pressure response throughout the pressurization process. Ambient temperature data is obtained through a digital temperature sensor deployed near the outer wall of the standard bottle, away from heat sources, with a sampling period of 1 second to ensure accurate reflection of the actual temperature changes during the test. The water injection flow rate signal is provided by an electromagnetic flowmeter or mass flowmeter connected in series on the outlet pipe of the water injection pump. Its output signal is converted from analog to digital and recorded synchronously with millisecond-level timestamps to accurately characterize the flow rate changes during the water injection phase. Once the system is pressurized to the preset test pressure and enters the pressure stabilization phase, the pressure sensor output signal is continuously monitored for at least 60 seconds. A pressure fluctuation sequence during the pressure stabilization phase is extracted. This sequence is defined as all continuous pressure sampling points from the moment the pressure first stabilizes within ±0.5% of the target value until the end of the pressure stabilization phase, used to characterize the system's minute pressure drift and noise characteristics under static pressure holding conditions. The above four types of signals—pressure sensor output signal, ambient temperature data, water injection flow signal, and pressure fluctuation sequence during the pressure stabilization phase—are all time-aligned and synchronously stored by the central data processing unit through a unified clock source, ensuring that each physical quantity strictly corresponds in the time dimension, and providing a highly consistent and highly synchronous original data foundation for subsequent multi-factor coupling error analysis.

[0049] Step 2: Based on the pressure sensor output signal, ambient temperature data, water injection flow signal, and pressure fluctuation sequence during the pressure stabilization phase, obtain three systematic error values ​​that affect the calibration accuracy. These three systematic error values ​​include: the nonlinear drift of the pressure sensor within the current operating range, the equivalent volume offset caused by temperature changes, and the deformation correction term introduced by human operation.

[0050] Step 211: Determine the real-time pressure value during the current calibration process based on the pressure sensor output signal;

[0051] It is worth noting that, in step 211, firstly, continuous voltage or current analog data for the pressurization stage and the initial stage of pressure stabilization are extracted from the pressure sensor output signal synchronously acquired and time-aligned in step 1. Then, this raw signal is input into a preset pressure-to-electrical signal conversion model. This model is a linear or piecewise linear mapping relationship established based on the factory calibration parameters of the pressure sensor, used to convert the electrical signal into pressure values ​​in engineering units. Next, the converted pressure sequence is subjected to moving average filtering with a window length of 50 sampling points to suppress high-frequency noise interference while retaining the main trend characteristics of pressure changes. Based on this, the starting moment of the system entering the pressure stabilization stage is identified, and the average of the filtered pressure values ​​within the first 10 seconds after that moment is taken as the real-time pressure value in the current calibration process. This real-time pressure value represents the stable working pressure that the standard bottle withstands under the current test conditions. Its accuracy is guaranteed by the aforementioned filtering and averaging strategies, effectively reflecting the actual pressure level and providing a reliable benchmark for subsequent division of pressure sub-intervals and calculation of nonlinear drift. The entire process is automatically completed by the embedded control unit of the hydrostatic testing device, ensuring that the acquisition of real-time pressure values ​​has high timeliness, low latency and good anti-interference ability, and that all intermediate data are consistent with the timestamp of the original acquisition signal, meeting the strict requirements of data synchronization for subsequent error analysis.

[0052] Step 212: Call the historical calibration database. The historical calibration database stores at least two sets of calibration records. Each set of calibration records contains a known standard pressure value and the pressure sensor output signal corresponding to the known standard pressure value.

[0053] It is worth noting that during step 212, the system first accesses the historical calibration database stored locally or deployed in the cloud through the embedded control unit or host computer software platform of the hydrostatic testing device. This database is organized using a structured data format (such as SQLite, MySQL, or an industrial time-series database), where each calibration record uses a unique identifier for the standard bottle, a calibration date and timestamp, ambient temperature, pressure range, and sensor model as index fields to ensure rapid retrieval and matching. The retrieval process is automatically triggered by the current calibration task. The system filters historical calibration records that meet preset similarity conditions based on the ID of the currently used standard bottle, the pressure sensor model, and the current ambient temperature range. The calibration records must contain at least two sets of valid calibration data completed under the same or similar operating conditions. Each calibration record must explicitly store the known standard pressure value (unit: MPa) applied to the standard bottle by the high-precision pressure reference device, and the pressure sensor output signal (unit: V or mA) synchronously acquired and calibrated at the same pressure stabilization time. The two must be strictly time-aligned and stored in pairs. Database calls are implemented through a standardized API interface, supporting conditional filtering by pressure range, time window, or error type, and returning a set of calibration records that meet the requirements. Finally, the call results are loaded into memory in the form of a structured array for use in subsequent step 213 for sub-range division and endpoint association.

[0054] Step 213: Based on at least two sets of calibration records in the historical calibration database, divide the measurement range of the pressure sensor into at least two continuous sub-intervals, and associate the endpoints of each sub-interval with a set of known standard pressure values ​​and the pressure sensor output signal corresponding to the known standard pressure values.

[0055] Step 214: When the real-time pressure value falls into any sub-interval, extract the pressure sensor output signal under the same known standard pressure value in the three most recent historical calibration databases within the current sub-interval, and calculate the average value. At the same time, combine the current pressure sensor output signal and solve the theoretical pressure value through a joint algorithm of local linear interpolation and least squares fitting. Use the difference between the theoretical pressure value and the real-time pressure value as the nonlinear drift of the pressure sensor in the current working interval.

[0056] It is worth noting that, when performing step 214, the sub-interval into which the real-time pressure value determined in step 211 falls during the current calibration process is first determined. This sub-interval has been divided and associated with the known standard pressure values ​​at its endpoints and their corresponding pressure sensor output signals in step 213 based on the historical calibration database. Subsequently, the same known standard pressure value (with an allowable tolerance of ±0.1 MPa) that is closest to the current real-time pressure value within this sub-interval is retrieved from the historical calibration database, and the pressure sensor output signals recorded at this standard pressure in the three most recent valid historical calibrations are extracted. The arithmetic mean of these three output signals is calculated to obtain the average historical sensor output value at this pressure point. Then, this average historical sensor output value and the current pressure sensor output signal are used together as input to construct a local linear mapping model: using the two endpoints of the sub-interval (known standard pressure values, corresponding to the average sensor output signals) as two reference points, linear interpolation is used to initially estimate the theoretical pressure value corresponding to the current output signal. To further improve accuracy, a least squares fitting algorithm is introduced on this basis—using the sub-interval... The known standard pressure value and average sensor output signal of all historical calibration points (including endpoints and internal points) are used as a sample set. An optimal local linear regression line is fitted, and its slope and intercept are determined by minimizing the sum of squared residuals. Finally, the current pressure sensor output signal is substituted into the regression equation to solve for the corresponding theoretical pressure value. This theoretical pressure value represents the real pressure level that the current output signal should correspond to after eliminating the influence of sensor nonlinear drift. Finally, the difference between the theoretical pressure value and the real-time pressure value obtained in step 211 is calculated, and this difference is defined as the nonlinear drift of the pressure sensor in the current operating range.

[0057] Step 221: Based on the ambient temperature data, query the pre-stored functional relationship between the bulk elastic modulus of water and temperature, and calculate the volume compressibility coefficient of water at the current temperature;

[0058] It is worth noting that, during step 221, the stable ambient temperature value during the current calibration process is first extracted from the ambient temperature data synchronously collected in step 1. This value is typically the average value of the ambient temperature sensor output within 30 seconds before the start of the pressure stabilization phase, to eliminate instantaneous fluctuation interference. Subsequently, the water medium physical property database pre-stored in the water pressure testing device's storage unit is accessed. This database stores the functional relationship between the water medium's bulk elastic modulus and temperature in the form of lookup tables or piecewise functions, covering the conventional test temperature range of 0℃ to 50℃. The data originates from high-precision experimental calibration results. Then, based on the current environment... The temperature value is used for interpolation lookup within the functional relationship. If linear interpolation is used, the two adjacent temperature nodes and their corresponding bulk modulus values ​​are located, and the bulk modulus at the current temperature is calculated proportionally. Then, based on the obtained bulk modulus, the volume compressibility coefficient of water at the current temperature is calculated through pure mathematical operations. The calculation method is as follows: divide 1 by the bulk modulus of water at the current temperature, and the quotient is the volume compressibility coefficient of water. This coefficient represents the relative change rate of water volume caused by a unit pressure change and is a key parameter for subsequent calculation of the compressibility volume change of water due to pressure.

[0059] Step 222: Obtain the reference volume, thermal expansion coefficient of the material, and preset reference temperature of the standard bottle, and calculate the change in thermal expansion volume of the standard bottle due to the deviation of the ambient temperature from the preset reference temperature based on the ambient temperature data, preset reference temperature, thermal expansion coefficient of the material, and reference volume.

[0060] It is worth noting that, during step 222, the reference volume (i.e., the nominal volume of the standard bottle at the reference temperature, in milliliters or cubic centimeters) and the coefficient of thermal expansion of the material (in degrees Celsius) are first read from the electronic identification tag of the standard bottle. Both of these parameters are precisely calibrated and stored at the factory. Simultaneously, a preset reference temperature is obtained. This reference temperature is typically 20 degrees Celsius and is the standard ambient temperature upon which the reference volume of the standard bottle is defined; it is pre-configured in the calibration parameter library of the hydrostatic testing device. Subsequently, the stable ambient temperature value during the current calibration process is extracted from the ambient temperature data collected in step 1. This value is taken as the average value over a period of time before the start of the pressure stabilization phase to ensure representativeness. Then, the ambient temperature is calculated relative to the preset... The temperature difference between the reference temperatures is obtained by subtracting the preset reference temperature from the current ambient temperature. Based on this, the change in thermal expansion volume of the standard bottle caused by the deviation of the ambient temperature from the preset reference temperature is calculated through pure mathematical operations. The calculation method is as follows: multiply the reference volume by the coefficient of thermal expansion of the material, and then multiply by the temperature deviation. The product is the change in thermal expansion volume. This change can be positive (volume expands when the ambient temperature is higher than the reference temperature) or negative (volume contracts when the ambient temperature is lower than the reference temperature), which accurately reflects the geometric volume drift of the standard bottle body caused by temperature changes. The final output of the change in thermal expansion volume will be used as a key component of the algebraic superposition in step 223 to construct a complete temperature-change equivalent volume offset model.

[0061] Step 223: Algebraically superimpose the volume compression effect of water with the thermal expansion volume change of the standard bottle to obtain the equivalent volume shift caused by temperature change;

[0062] Step 231: Calculate the rate of change of water injection rate during the pressurization stage based on the water injection flow signal;

[0063] It is worth noting that, during step 231, the complete flow time series of the pressurization stage is first extracted from the water injection flow signal synchronously acquired in step 1. This series is output in real time by a high-precision flow meter installed on the water injection pump outlet pipeline at a sampling frequency of no less than 50 times per second. Subsequently, the start and end times of the pressurization stage are identified. The start time is defined as the time when the water injection pump starts and the flow rate first exceeds a preset threshold (e.g., 0.5 liters per minute), and the end time is defined as the time when the pressure reaches the target test pressure and enters the pressure stabilization control mode. Within this time window, the water injection flow signal is processed by first-order numerical differentiation. Specifically, the flow difference between two adjacent sampling points is calculated sequentially. Divide the result by the corresponding time interval to obtain the instantaneous water injection rate change rate at each moment. To further suppress the influence of differential amplification noise, a moving average filter is applied to the obtained instantaneous water injection rate change rate sequence, with a window length of 20 sampling points. Finally, the maximum absolute value in the filtered sequence is taken as the water injection rate change rate during the pressurization stage. This value characterizes the severity of water injection rate fluctuations during operation—if the operation is stable, this value approaches zero; if there are sudden starts, stops, or changes in flow rate caused by manual intervention, this value increases significantly. The obtained water injection rate change rate will be used as one of the key input parameters of the human factor operation deviation model to quantify the impact of dynamic disturbances introduced by human operation on the measurement of standard bottle deformation.

[0064] Step 232: Determine the actual stabilization time required from the end of pressurization to the stabilization of pressure fluctuations based on the pressure fluctuation sequence during the stabilization phase;

[0065] It is worth noting that, in step 232, firstly, complete pressure-time data is extracted from the pressure fluctuation sequence of the stabilization phase synchronously acquired and time-aligned in step 1. This sequence begins at the end of pressurization (i.e., the moment when the system pressure first reaches the target test pressure and switches to the stabilization control mode) and continues until the preset total stabilization time (usually 60 or 120 seconds). Subsequently, a sliding standard deviation analysis is performed on the pressure fluctuation sequence: with a window length of 5 seconds and a step size of 1 second, the standard deviation of the pressure value within each window is calculated segment by segment to generate a fluctuation index sequence characterizing local pressure stability. Next, a pressure stability threshold pre-stored in the calibration parameter library is set. This threshold is determined based on the historical performance data of the hydrostatic testing device and is usually 0.1% of the full scale of the pressure sensor. Starting from the end of pressurization, the time axis is searched backward. Find the first starting time point that satisfies the condition that "the standard deviation of three consecutive sliding windows is less than or equal to the pressure stabilization threshold", and define this time point as the pressure fluctuation stabilization start time. Finally, calculate the time interval between the end of pressurization and the start time of pressure fluctuation stabilization. The result is the actual pressure stabilization time required from the end of pressurization to the stabilization of pressure fluctuation. This time reflects the response time required for the system to reach dynamic equilibrium under the current operating conditions. If the operation is standardized and the water injection is stable, the actual pressure stabilization time is shorter. If there are human factors such as excessively rapid pressurization, water hammer effect, or insufficient venting, the pressure fluctuation decays slowly, and the actual pressure stabilization time is significantly prolonged. The obtained actual pressure stabilization time will be used as another key input parameter of the human factor operation deviation model, and together with the water injection rate change rate obtained in step 231, it will be used to quantify the deformation correction term introduced by human operation.

[0066] Step 233: Input the water injection rate change rate and the actual pressure stabilization time as input parameters into the pre-trained human factor operation bias model, and output the deformation correction term introduced by human operation;

[0067] It is worth noting that during step 233, a pre-trained human factor bias model is invoked. This model maps the rate of change of water injection rate obtained in step 231 and the actual pressure stabilization time obtained in step 232 to a deformation correction term introduced by human operation. To ensure the scientific validity and generalization ability of this model, its training process strictly follows the following feasible procedure:

[0068] First, a training dataset is constructed, consisting of a large number of paired calibration samples accumulated from historical calibration tasks. Each sample contains two input features and one output label:

[0069] Input feature one is the rate of change of water injection rate (unit: liters per minute per second) calculated in the corresponding calibration task, which is extracted from the historical water injection flow signal using the same method as in step 231;

[0070] Input feature 2 is the actual stabilization time (unit: seconds) determined in the corresponding calibration task, which is obtained by the same fluctuation stability determination algorithm as in step 232;

[0071] The training label is the volume measurement deviation value caused by human operation, which is confirmed by a high-precision benchmark method (such as internal measurement or verification by a third-party metrology institution) in this calibration. It is called the "correction term for the actual deformation introduced by human operation" (unit: milliliters). This label is obtained in the following way: In a controlled experiment, the same operator repeatedly performs external hydrostatic tests on the same standard bottle under the same environmental conditions. One test uses ideal automated operation (as the benchmark), and the rest use different styles of manual operation. The difference between the deformation of the standard bottle obtained by manual operation and the result of automated benchmark is regarded as the deformation correction term introduced by this operation and is used as the truth label for supervised learning.

[0072] Secondly, the model structure is selected. Considering the low input dimensionality (only 2 dimensions), clear nonlinear relationships, and the need to balance real-time performance, a shallow neural network (such as a multilayer perceptron with one hidden layer and 10 neurons) or a support vector regression (SVR) model is adopted. The model hyperparameters include: learning rate (set to 0.001), loss function (mean squared error), regularization coefficient (L2 regularization, coefficient is 0.01), maximum number of training epochs (500 epochs), and an early stopping mechanism (terminating the training if the verification loss does not decrease for 20 consecutive epochs).

[0073] Next, model training and validation are performed. Historical data is divided into training, validation, and test sets in an 8:1:1 ratio. During training, the Adam optimizer is used to minimize the error between the predicted values ​​and the true labels. Hyperparameters are adjusted using the validation set to prevent overfitting. Finally, the model performance is evaluated on the test set, requiring the mean absolute error to be no more than 0.05 ml and the coefficient of determination R² to be greater than 0.92. After the model training is completed, it is solidified into a lightweight inference module and deployed in the embedded system of the hydrostatic testing device.

[0074] When performing step 233 in the current calibration task, this embodiment uses the water injection rate change rate and actual pressure stabilization time obtained in this calculation as input vectors and feeds them into the pre-trained model. The model calculates through forward propagation and outputs a scalar value, which is the deformation correction term introduced by human operation. The correction term can be a positive value (indicating that the operation caused the measured deformation to be too large, which needs to be subtracted) or a negative value (indicating that the measured deformation was too small, which needs to be added). The output result is automatically appended with the current task ID, timestamp, and confidence index (based on whether the input features are within the training distribution range) and sent to step 4 to participate in the final compensation calculation.

[0075] Step 3: Perform validity analysis on each systematic error value, and obtain the error validity coefficient for each systematic error value based on the analysis results;

[0076] Step 31: Retrieve the historical error distribution dataset for each systematic error value;

[0077] It is worth noting that when executing step 31, this embodiment calls up the historical error distribution dataset that strictly corresponds to its error type for each systematic error value obtained in the current calibration process (including the nonlinear drift of the pressure sensor in the current working range, the equivalent volume offset caused by temperature change, and the deformation correction term introduced by human operation). The detailed implementable process is as follows:

[0078] First, the type of the current systematic error value is identified—if it is a nonlinear drift, it is associated with the "Sensor Nonlinear Error History Database"; if it is an equivalent volume offset, it is associated with the "Temperature Coupling Error History Database"; if it is a human operation correction item, it is associated with the "Human Operation Deviation History Database". Each type of historical error distribution dataset is stored in a structured form in local solid-state storage or calibration parameter library, using a key-value pair indexing mechanism. The primary key includes the standard bottle ID, ambient temperature range, pressure operating range, and operator number (if applicable), ensuring the accuracy of data matching.

[0079] Secondly, extract the key context parameters for the current calibration task: for nonlinear drift, extract the current pressure sub-range and sensor model; for temperature shift, extract the range of difference between the current ambient temperature and the reference temperature; for human error correction items, extract the operator ID (if the system supports identity recognition) or assign it to the general operation group by default. Based on these parameters, perform a conditional query in the corresponding historical error distribution dataset to filter out all historical systematic error value records that meet similar operating conditions, requiring at least 30 valid records to ensure statistical significance.

[0080] Subsequently, the selected set of historical error values ​​is loaded into the memory buffer and the data is cleaned: records marked as abnormal or missing key metadata are removed; the remaining data is sorted in reverse chronological order, and high-confidence samples within the past year are retained first; finally, a historical error distribution dataset that highly matches the current error type and operating conditions is formed, which is used for statistical calculation of reasonable threshold ranges in subsequent step 32.

[0081] Step 32: Based on the historical error distribution dataset, determine a reasonable threshold range for each systematic error value, wherein the reasonable threshold range includes a lower limit and an upper limit.

[0082] It is worth noting that, when executing step 32, this embodiment, based on the historical error distribution dataset that has been called and cleaned in step 31, calculates the corresponding reasonable threshold range for each current systematic error value (including the nonlinear drift of the pressure sensor within the current operating range, the equivalent volume offset caused by temperature changes, and the deformation correction term introduced by human operation). The process of determining this range follows the detailed and feasible procedure below:

[0083] First, statistical analysis is performed on all historical systematic error values ​​in the historical error distribution dataset corresponding to the current error type. The sample mean and standard deviation of this dataset are calculated: the mean reflects the central tendency of this type of error under similar operating conditions, and the standard deviation characterizes its dispersion. To balance robustness and adaptability, a modified statistical method is adopted—if the dataset size is greater than or equal to 50 records, the arithmetic mean and unbiased standard deviation are used directly; if the dataset size is less than 50 records but not less than 30 records, the median is used instead of the mean, and the dispersion is estimated using the median absolute deviation (MAD), which is then converted into a robust estimate of the standard deviation using a coefficient of 1.4826.

[0084] Secondly, the threshold boundaries are dynamically set according to a preset confidence level. This confidence level is pre-configured by the calibration parameter library of the hydrostatic testing device, with a default value of 95%, corresponding to approximately ±1.96 standard deviations under a normal distribution. To simplify calculations and retain engineering margins, ±2 standard deviations are typically used as the default expansion factor. Therefore, the lower limit of a reasonable threshold range is calculated as: mean minus two standard deviations (or median minus two robust standard deviations), and the upper limit is calculated as: mean plus two standard deviations (or median plus two robust standard deviations). If the error involved is physically unidirectional (e.g., the human error correction should theoretically not exceed a certain safety limit), then hard boundary constraints should be applied to the upper and lower limits to ensure that the threshold range conforms to engineering realities.

[0085] Subsequently, the calculation results are validated for reasonableness: if the obtained interval width is less than the preset minimum tolerance (for example, the minimum tolerance for nonlinear drift is 0.01 MPa, and the volume offset is 0.02 mL), the interval width is automatically expanded to the minimum tolerance to avoid the threshold interval being too narrow and the misjudgment rate increasing due to the excessive concentration of historical data; if the distribution of historical data is obviously skewed (determined by skewness test), the quantile method can be selected to replace the mean ± standard deviation method, for example, using the 5th percentile as the lower limit and the 95th percentile as the upper limit, to better adapt to non-Gaussian distribution scenarios;

[0086] Finally, in this embodiment, the determined lower and upper limits are encapsulated into a reasonable threshold range for the current systematic error value, and cached together with metadata such as calculation method identifier, confidence level, and dataset size, for comparison and judgment in step 33.

[0087] Step 33: Compare each of the currently acquired systematic error values ​​with the lower limit and upper limit of the reasonable threshold range for each systematic error value;

[0088] Step 34: If the current systematic error value is within the reasonable threshold range, calculate the first error validity coefficient of the current systematic error value based on the reasonable threshold range;

[0089] Step 341: Extract the lower and upper limits of the reasonable threshold range for the current systematic error value;

[0090] Step 342: Based on the lower limit and upper limit of the reasonable threshold range of the current systematic error value, calculate the middle threshold and width parameter of the reasonable threshold range, wherein the middle threshold is the arithmetic mean of the lower limit and the upper limit, and the width parameter is the difference between the upper limit and the lower limit.

[0091] Step 343: Calculate the absolute deviation between the current systematic error value and the intermediate threshold;

[0092] It is worth noting that, when performing step 343, this embodiment uses the intermediate threshold (i.e., the arithmetic mean of the lower and upper limits of the reasonable threshold range to which the current systematic error value belongs) calculated in step 342 to perform deviation quantification processing on the systematic error value obtained in the current calibration process. The specific implementation process is as follows:

[0093] First, read the currently processed systematic error value from memory—this value has been calculated and stored in step 2, such as the nonlinear drift of the pressure sensor, the equivalent volume offset caused by temperature change, or the deformation correction term introduced by human operation; at the same time, read the corresponding intermediate threshold output by step 342, which represents the ideal center position where this type of error is most likely to occur under historical statistical distribution.

[0094] Subsequently, a numerical subtraction operation is performed: the current systematic error value is subtracted from the intermediate threshold to obtain a signed difference; in order to eliminate the directional influence and focus on the magnitude of the deviation, the system takes the absolute value of this difference to obtain the absolute deviation, which is a non-negative real number whose physical meaning is the deviation of the current error value from the historical distribution center, and the unit is consistent with the original systematic error value (such as MPa, mL, etc.).

[0095] Throughout the calculation process, double-precision floating-point operations are used to ensure numerical stability, and anomaly detection and handling are performed for possible overflows or invalid inputs (such as NaN or infinity): if an anomaly is detected, data resampling is triggered or the current error validity coefficient is marked as zero to prevent error propagation; after the calculation is completed, the obtained absolute deviation is written to a temporary variable buffer with a timestamp and error type identifier to ensure that it serves as the only valid input source for normalization processing in subsequent step 344.

[0096] Step 344: Normalize the absolute deviation to obtain the normalized absolute deviation, which is the ratio of the absolute deviation to the width parameter.

[0097] Step 345: Using the absolute deviation and the width parameter as input variables, substitute them into the preset interval validity function to calculate the first error validity coefficient of the current systematic error value;

[0098] It is worth noting that, when performing step 345, this embodiment uses the normalized absolute deviation obtained in step 344 as the core input variable, and substitutes it into a preset interval validity function to calculate the first error validity coefficient of the current systematic error value. This function is not temporarily defined, but is configured and fixed in the calibration parameter library before the hydrostatic testing device leaves the factory or during the initial calibration stage. Its form has been verified by a large number of experiments and optimized by engineering to ensure that the error confidence is smoothly, monotonically and physically clearly quantified within a reasonable threshold range.

[0099] Specifically, the preset validity function within the interval adopts the following Gaussian decay function form:

[0100] The first error effectiveness coefficient is equal to the output value of an exponential function with the natural constant as the base. The exponential part of the exponential function is -1 multiplied by the square of the normalized absolute deviation and then divided by twice the square of the adjustment factor. The adjustment factor is a dimensionless constant between 0.2 and 0.5, used to control the steepness of the effectiveness coefficient decay with the deviation. The default value is set to 0.35.

[0101] During implementation, the current configuration value of the adjustment factor is first read from the calibration parameter library. Then, the square of the normalized absolute deviation is calculated. Next, this squared value is divided by twice the square of the adjustment factor to obtain a non-negative real number. Then, the negative value of this real number is used as the exponent. Finally, the exponent function module in the embedded mathematics library is called to calculate the corresponding value of the natural exponent. The result is the first error validity coefficient. This coefficient strictly ranges from zero to one: when the normalized absolute deviation is zero (i.e., the current systematic error value is exactly equal to the intermediate threshold), the exponent part is zero, and the exponent function output is one, indicating complete confidence. As the normalized absolute deviation increases, the coefficient decreases smoothly and monotonically, but does not suddenly drop to zero, reflecting a gradual decay of confidence in edge data within a reasonable range.

[0102] The first error validity coefficient obtained is used for the fusion calculation in step 4, thereby achieving sufficient retention of high-confidence error terms and moderate suppression of low-confidence error terms.

[0103] Step 35: If the current systematic error value is less than the lower limit of the reasonable threshold range, then calculate the second error effectiveness coefficient of the current systematic error value based on the reasonable threshold range and the first preset attenuation rule;

[0104] Step 351: Extract the lower limit and width parameters of the reasonable threshold range for the current systematic error value;

[0105] Step 352: Calculate the negative deviation between the current systematic error value and the lower limit value, wherein the negative deviation is the lower limit value minus the current systematic error value;

[0106] Step 353: Normalize the negative deviation to obtain a normalized negative deviation, wherein the normalized negative deviation is the ratio of the negative deviation to the width parameter.

[0107] Step 354: Substitute the normalized negative deviation into the first preset attenuation rule, where the first preset attenuation rule is a preset first attenuation function, and calculate the second error effectiveness coefficient.

[0108] It is worth noting that, in executing step 354, this embodiment uses the normalized negative deviation calculated in step 353 as an input variable, and substitutes it into a preset first attenuation function to calculate the second error validity coefficient of the current systematic error value. This function is specifically designed to handle abnormal or marginal error situations below the lower limit of a reasonable threshold range. Its form has been determined by fitting a large amount of historical calibration data before the deployment of the hydrostatic testing device and is fixed in the calibration parameter library, ensuring that the error reliability is reasonably, stably and physically meaningfully attenuated in the negative over-limit region.

[0109] Specifically, the preset first attenuation function adopts the following rational fractional attenuation model:

[0110] The second error effectiveness coefficient is equal to the quotient of one divided by the sum of the products of the normalized negative deviation and the attenuation slope coefficient; wherein, the attenuation slope coefficient is a dimensionless constant greater than zero, used to adjust the rate at which the effectiveness coefficient decreases as the negative deviation increases, with a default value of 1.5, which can be configured independently in the parameter library according to different error types (such as sensor drift or human factors operation).

[0111] In the detailed implementation process, firstly, the attenuation slope coefficient matching the current systematic error type is read from the calibration parameter library; then, this coefficient is multiplied by the normalized negative deviation output in step 353 to obtain a non-negative real number; next, one is added to this product to form the denominator; finally, the reciprocal operation is performed, that is, one is divided by the denominator, and the result is the second error validity coefficient. This coefficient always satisfies the following characteristics: when the normalized negative deviation is zero (that is, the current error value is exactly equal to the lower limit), the second error validity coefficient is one, realizing the continuous connection with the calculation logic within the interval; as the normalized negative deviation increases (that is, the error value is lower than the lower limit), the coefficient monotonically decreases and asymptotically approaches zero, but never becomes negative, reflecting the gradual deweighting of severely negative abnormal data rather than direct elimination;

[0112] The final output of the second error validity coefficient is passed to step 4, and together with other error terms and their validity coefficients and weighting coefficients, it participates in the fusion calculation of the calibrated deformation of the standard bottle after compensation.

[0113] Step 36: If the current systematic error value is greater than the upper limit of the reasonable threshold range, calculate the third error effectiveness coefficient of the current systematic error value based on the reasonable threshold range and the second preset attenuation rule;

[0114] It is worth noting that in this embodiment, steps 31 to 36 represent a fundamental shift from static error compensation to dynamic reliability assessment. By accessing historical error distribution datasets and determining reasonable threshold ranges accordingly, it is possible to objectively identify whether the current error value is within the normal fluctuation range. Furthermore, based on its relative position to the upper and lower limits of the range, the calculation path for the first, second, or third error validity coefficients is intelligently selected. This mechanism completely abandons the crude approach of simply discarding or fully adopting out-of-limit errors in traditional methods, and instead establishes a continuous reliability quantification system based on statistical laws. More importantly, this step provides a scientific basis for subsequent weighted compensation—high reliability error terms are fully retained, low reliability terms are reasonably suppressed, and marginal data achieves value mining through gradual decay. As a result, not only is the robustness of error compensation significantly improved, but the system's adaptability in the face of complex working conditions such as sensor aging, sudden environmental changes, or operational anomalies is enhanced, laying a highly reliable decision-making foundation for the entire calibration process.

[0115] Step 361: Extract the upper limit and width parameters of the reasonable threshold range for the current systematic error value;

[0116] Step 362: Calculate the positive deviation between the current systematic error value and the upper limit value, wherein the positive deviation is the current systematic error value minus the upper limit value;

[0117] Step 363: Normalize the positive deviation to obtain a normalized positive deviation, wherein the normalized positive deviation is the ratio of the positive deviation to the width parameter;

[0118] Step 364: Substitute the normalized positive deviation into the preset second decay function to calculate the third error effectiveness coefficient;

[0119] It is worth noting that, in executing step 364, this embodiment uses the normalized positive deviation calculated in step 363 as an input variable, and substitutes it into a preset second decay function to calculate the third error validity coefficient of the current systematic error value. This function is specifically designed to handle positive over-limit situations that exceed the upper limit of the reasonable threshold range. Its design fully considers the potential harm of positive anomalies (such as sudden positive drift of the pressure sensor, overestimation of volume expansion due to a sudden temperature rise, or false deformation caused by excessive operation) to system calibration, and achieves controllable suppression of high-risk error terms through a smooth decay mechanism. This function form has been regression-fitted and engineering-verified based on a large amount of historical over-limit calibration data before the device is deployed, and has been fixed as a parameter in the calibration parameter library of the hydrostatic testing device.

[0120] Specifically, the preset second decay function adopts the following exponential decay model:

[0121] The third error effectiveness coefficient is equal to the output value of an exponential function with the natural constant as the base. The exponent of this exponential function is -1 multiplied by the normalized positive deviation and then multiplied by the positive decay rate coefficient. The positive decay rate coefficient is a dimensionless constant greater than zero, with a default value of 0.8. It can be configured independently in the parameter library according to the error type (such as temperature deviation or human operation) and is used to adjust the rate at which the effectiveness coefficient decays as the positive deviation increases.

[0122] In the detailed implementation process, the positive decay rate coefficient corresponding to the current systematic error type is first read from the calibration parameter library. Then, this coefficient is multiplied by the normalized positive deviation output in step 363 to obtain a non-negative real number. Next, the negative value of this product is taken as the exponent. Finally, the natural exponent function module in the embedded mathematical library is called to calculate the function value corresponding to this exponent, and the result is the third error validity coefficient. This coefficient has clear physical characteristics: when the normalized positive deviation is zero (i.e., the current error value is exactly equal to the upper limit), the exponent part is zero, and the exponent function output is one, ensuring continuous connection with the calculation logic within the interval and at the lower limit; as the normalized positive deviation increases (i.e., the error value is higher than the upper limit), the coefficient monotonically decreases and approaches zero, but always remains positive, reflecting a gradual weighting strategy for severely positive abnormal data, avoiding information abrupt changes or system oscillations caused by hard truncation.

[0123] The final generated third error validity coefficient will be sent to step 4 for fusion calculation.

[0124] Step 4: Based on each systematic error value, the error effectiveness coefficient of each systematic error value, and the preset weighting coefficient of each systematic error value, obtain the compensated standard bottle calibration deformation amount;

[0125] It is worth noting that, in step 4, this embodiment calculates the compensated standard bottle calibration deformation amount through weighted fusion based on each systematic error value, its corresponding error validity coefficient (i.e., the first, second, or third error validity coefficient), and the preset weight coefficient associated with each systematic error value. The preset weight coefficients are set strictly according to the principle of objectivity, generated entirely based on historical data and statistical analysis methods, without relying on expert experience or subjective manual assignment. The specific implementation process is as follows:

[0126] First, during the initial deployment phase or periodic maintenance cycle of the hydrostatic testing device, an independent weight coefficient training module is invoked. This module constructs a training set based on high-quality calibration records accumulated in the historical calibration database. Each record contains three systematic error values ​​(nonlinear drift, temperature change equivalent volume offset, and human-induced deformation correction term) and their corresponding true total error (i.e., the deformation of the standard bottle before compensation, i.e., the difference between the original standard bottle calibration deformation and the high-precision reference value).

[0127] Next, a multiple linear regression model was used to fit the above data: using the three systematic error values ​​as independent variables and the true total error as the dependent variable, the optimal regression coefficients were solved using the least squares method. The absolute values ​​of the obtained regression coefficients were normalized (i.e., each was divided by the sum of the absolute values ​​of the three), and these became the initial weight coefficients for the three systematic error values. This process ensures that the weights reflect the actual contribution of each error source to the total error and have clear statistical and physical meaning.

[0128] To further enhance robustness, a cross-validation mechanism is introduced: historical data is randomly divided into five groups, with four groups used for training and one group for validation, repeated five times, and the mean of the weight coefficients of each error term is taken as the final value; at the same time, if the coefficient of a certain error term is close to zero in multiple regressions (e.g., p-value greater than 0.05), its weight is automatically set to the minimum allowable value (e.g., 0.05) to avoid invalid terms dominating compensation;

[0129] The three finalized weighting coefficients are written into the calibration parameter library, and the generation time, dataset size, and model R² value are marked for subsequent auditing. Each time step 4 is executed, the set of objectively generated preset weighting coefficients is first read from the parameter library and multiplied by the current systematic error values ​​and their error validity coefficients to obtain the three weighted correction amounts. Then, the original standard bottle calibration deformation is subtracted from these three weighted correction amounts (or algebraically superimposed according to the error definition direction) to obtain the compensated standard bottle calibration deformation.

[0130] It is worth further elaborating that in the multi-factor coupled error compensation calibration method constructed in this embodiment, there is a clear and reasonable functional distinction between the error validity coefficient and the systematic error value: the error validity coefficient does not change the numerical value or physical essence of the systematic error value itself, but rather dynamically quantifies and evaluates its reliability or reference value under the current operating conditions. Specifically, the systematic error value (including the nonlinear drift of the pressure sensor in the current operating range, the equivalent volume offset caused by temperature changes, and the deformation correction term introduced by human operation) is an objective deviation calculated by a physical model or data-driven method based on the real-time collected pressure sensor output signal, ambient temperature data, water injection flow signal, and pressure fluctuation sequence during the pressure stabilization phase. Its value itself truly reflects the systematic influence existing under the current test conditions. The error validity coefficient (i.e., the first, second, or third error validity coefficient) is a reliability factor between 0 and 1 dynamically generated by normalizing the deviation and using a preset function (such as Gaussian, rational fraction, or exponential decay function) based on the relative position of the error value with the reasonable threshold range determined by the historical error distribution. This factor is used to adjust the participation of the error value in the final compensation calculation—when it is close to 1, it indicates that the error value is within the normal historical fluctuation range and should be fully adopted; when it approaches 0, it indicates that the error value may be affected by abnormal interference, and its impact should be significantly suppressed. Therefore, the role of the error validity coefficient is not to correct the error value itself, but to achieve differentiated fusion processing of error data at different confidence levels, thereby avoiding overcompensation due to outliers and improving the robustness of the overall calibration results.

[0131] Meanwhile, the error validity coefficient and the preset weight coefficient are two completely different technical elements in this embodiment, with entirely different properties, sources, and mechanisms of action. They should not be confused, nor do they overlap in concept. The preset weight coefficient is a constant objectively determined through multiple regression analysis of historical calibration data during device initialization or periodic maintenance. It reflects the inherent proportion of the three types of systematic error sources on the total calibration deviation, possessing long-term stability and structural significance. The error validity coefficient, on the other hand, is a variable generated in real-time during each calibration task, reflecting the instantaneous reliability of the current specific error value in this experimental context, exhibiting strong dynamism and data dependence. In the compensation calculation in step 4, the two work synergistically in a product form: the preset weight coefficient reflects "which type of error is more critical in terms of physical mechanism," while the error validity coefficient reflects "whether this error value is trustworthy." This dual-factor fusion mechanism retains the prior importance of the error source while incorporating the posterior credibility of a single measurement, achieving an organic combination of static mechanism understanding and dynamic data quality assessment. Therefore, clearly distinguishing and combining the two is not only logically consistent but also significantly enhances the scientific rigor and engineering adaptability of the compensation model.

[0132] Step 5: Use the compensated standard bottle's calibrated deformation as the final calibration value of the standard bottle, use the final calibration value of the standard bottle to calibrate the hydrostatic testing device, and update the calibration parameter library of the hydrostatic testing device simultaneously.

[0133] It is worth noting that, in step 5, this embodiment formally establishes the compensated standard bottle calibration deformation calculated in step 4 as the final calibration value of the standard bottle in this calibration task, and uses this as the core basis to complete the calibration of the hydrostatic testing device and the update of the parameter library. This process strictly follows metrological specifications, and the specific implementation is as follows:

[0134] First, the compensated standard bottle calibration deformation is written into the electronic identification tag (such as an RFID chip or QR code associated with a database) of the current standard bottle as its latest valid calibration result under the current environment and operating conditions, for subsequent traceability and comparison; at the same time, this value is marked as "verified high confidence calibration value" and is accompanied by metadata such as timestamp, ambient temperature, operator ID (if applicable) and three error validity coefficients to ensure traceability throughout the entire life cycle;

[0135] Subsequently, the calibration process of the hydrostatic testing device is initiated: the final calibration value is compared with the theoretical reference volume of the standard bottle, and the system deviation of the current device in the pressure-volume conversion model is calculated; based on this deviation, the calibration parameters inside the hydrostatic testing device are automatically adjusted, including but not limited to the pressure-volume proportional coefficient, the system stiffness compensation term, and the reference offset in the multi-factor coupling error compensation model; the updates of these parameters are realized through a closed-loop feedback mechanism to ensure that the device can output high-precision deformation results after dynamic correction when conducting hydrostatic tests on the gas cylinders under test in subsequent tests;

[0136] Next, the calibration parameter library is updated synchronously: all key data generated in this calibration—including three systematic error values, corresponding error validity coefficients, reasonable threshold ranges, weight coefficient usage records, and updated device calibration parameters—are packaged and stored in the calibration parameter library locally or in the cloud; at the same time, the newly added data will serve as new samples for calling historical error distribution datasets in future step 31, continuously optimizing the statistical basis of reasonable threshold ranges, and forming a closed-loop intelligent evolution system of "calibration—compensation—calibration—learning";

[0137] This not only achieves high-precision solidification of single calibration results, but also promotes the evolution of the entire testing system towards intelligent self-adaptation, self-correction, and self-optimization, significantly improving the long-term stability and cross-cycle consistency of gas cylinder hydrostatic testing.

[0138] It should be noted that the terminology used in this invention is for describing specific embodiments only and is not intended to limit the scope of this application. As shown in this specification, unless the context clearly indicates otherwise, words such as "a," "an," "an," and / or "the" do not specifically refer to the singular and may include the plural. The terms "comprising," "including," or any other variations thereof are intended to cover a non-exclusive inclusion, such that a process, method, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, or apparatus that includes said element.

[0139] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the technical solutions of the embodiments of the present invention.

Claims

1. A multi-factor coupling error compensation calibration method for external hydrostatic testing of gas cylinders, characterized in that, Includes the following steps: Step 1: Install the standard bottle into the water pressure testing device and simultaneously collect the pressure sensor output signal, ambient temperature data, water injection flow signal, and pressure fluctuation sequence during the pressure stabilization phase. Step 2: Based on the pressure sensor output signal, ambient temperature data, water injection flow signal, and pressure fluctuation sequence during the pressure stabilization phase, obtain the three systematic error values ​​that affect the calibration accuracy; The three systematic error values ​​that affect the calibration accuracy include: the nonlinear drift of the pressure sensor in the current working range, the equivalent volume offset caused by temperature change, and the deformation correction term introduced by human operation. Step 211: Determine the real-time pressure value during the current calibration process based on the pressure sensor output signal; Step 212: Call the historical calibration database. The historical calibration database stores at least two sets of calibration records. Each set of calibration records contains a known standard pressure value and the pressure sensor output signal corresponding to the known standard pressure value. Step 213: Based on at least two sets of calibration records in the historical calibration database, divide the measurement range of the pressure sensor into at least two continuous sub-intervals, and associate the endpoints of each sub-interval with a set of known standard pressure values ​​and the pressure sensor output signal corresponding to the known standard pressure values. Step 214: When the real-time pressure value falls into any sub-interval, extract the pressure sensor output signal under the same known standard pressure value in the three most recent historical calibration databases within the current sub-interval, and calculate the average value. At the same time, combine the current pressure sensor output signal and solve the theoretical pressure value through a joint algorithm of local linear interpolation and least squares fitting. Use the difference between the theoretical pressure value and the real-time pressure value as the nonlinear drift of the pressure sensor in the current working interval. Step 221: Based on the ambient temperature data, query the pre-stored functional relationship between the bulk elastic modulus of water and temperature, and calculate the volume compressibility coefficient of water at the current temperature; Step 222: Obtain the reference volume, thermal expansion coefficient of the material, and preset reference temperature of the standard bottle, and calculate the change in thermal expansion volume of the standard bottle due to the deviation of the ambient temperature from the preset reference temperature based on the ambient temperature data, preset reference temperature, thermal expansion coefficient of the material, and reference volume. Step 223: Algebraically superimpose the volume compression effect of water with the thermal expansion volume change of the standard bottle to obtain the equivalent volume shift caused by temperature change; Step 231: Calculate the rate of change of water injection rate during the pressurization stage based on the water injection flow signal; Step 232: Determine the actual stabilization time required from the end of pressurization to the stabilization of pressure fluctuations based on the pressure fluctuation sequence during the stabilization phase; Step 233: Input the water injection rate change rate and the actual pressure stabilization time as input parameters into the pre-trained human factor operation bias model, and output the deformation correction term introduced by human operation; Step 3: Perform validity analysis on each systematic error value, and obtain the error validity coefficient for each systematic error value based on the analysis results; Step 4: Based on each systematic error value, the error effectiveness coefficient of each systematic error value, and the preset weighting coefficient of each systematic error value, obtain the compensated standard bottle calibration deformation amount; Step 5: Use the compensated standard bottle's calibrated deformation as the final calibration value of the standard bottle, use the final calibration value of the standard bottle to calibrate the hydrostatic testing device, and update the calibration parameter library of the hydrostatic testing device simultaneously.

2. The multi-factor coupling error compensation calibration method for external hydrostatic testing of gas cylinders according to claim 1, characterized in that, The process of performing validity assessment analysis on each systematic error value and obtaining the error validity coefficient for each systematic error value based on the analysis results includes: Step 31: Retrieve the historical error distribution dataset for each systematic error value; Step 32: Based on the historical error distribution dataset, determine a reasonable threshold range for each systematic error value, wherein the reasonable threshold range includes a lower limit and an upper limit. Step 33: Compare each of the currently acquired systematic error values ​​with the lower limit and upper limit of the reasonable threshold range for each systematic error value; Step 34: If the current systematic error value is within the reasonable threshold range, calculate the first error validity coefficient of the current systematic error value based on the reasonable threshold range; Step 35: If the current systematic error value is less than the lower limit of the reasonable threshold range, then calculate the second error effectiveness coefficient of the current systematic error value based on the reasonable threshold range and the first preset attenuation rule; Step 36: If the current systematic error value is greater than the upper limit of the reasonable threshold range, calculate the third error effectiveness coefficient of the current systematic error value based on the reasonable threshold range and the second preset attenuation rule.

3. The multi-factor coupling error compensation calibration method for external hydrostatic testing of gas cylinders according to claim 2, characterized in that, The first error validity coefficient, calculated based on the reasonable threshold range, for the current systematic error value includes: Step 341: Extract the lower and upper limits of the reasonable threshold range for the current systematic error value; Step 342: Based on the lower limit and upper limit of the reasonable threshold range of the current systematic error value, calculate the middle threshold and width parameter of the reasonable threshold range, wherein the middle threshold is the arithmetic mean of the lower limit and the upper limit, and the width parameter is the difference between the upper limit and the lower limit. Step 343: Calculate the absolute deviation between the current systematic error value and the intermediate threshold; Step 344: Normalize the absolute deviation to obtain the normalized absolute deviation, which is the ratio of the absolute deviation to the width parameter. Step 345: Using the absolute deviation and the width parameter as input variables, substitute them into the preset interval validity function to calculate the first error validity coefficient of the current systematic error value.

4. The multi-factor coupling error compensation calibration method for external hydrostatic testing of gas cylinders according to claim 2, characterized in that, The second error validity coefficient, calculated based on the reasonable threshold range and the first preset attenuation rule, for the current systematic error value includes: Step 351: Extract the lower limit and width parameters of the reasonable threshold range for the current systematic error value; Step 352: Calculate the negative deviation between the current systematic error value and the lower limit value, wherein the negative deviation is the lower limit value minus the current systematic error value; Step 353: Normalize the negative deviation to obtain a normalized negative deviation, wherein the normalized negative deviation is the ratio of the negative deviation to the width parameter. Step 354: Substitute the normalized negative deviation into the first preset attenuation rule, where the first preset attenuation rule is a preset first attenuation function, and calculate the second error effectiveness coefficient.

5. The multi-factor coupling error compensation calibration method for external hydrostatic testing of gas cylinders according to claim 2, characterized in that, The calculation of the third error validity coefficient based on the reasonable threshold range and the second preset attenuation rule for the current systematic error value includes: Step 361: Extract the upper limit and width parameters of the reasonable threshold range for the current systematic error value; Step 362: Calculate the positive deviation between the current systematic error value and the upper limit value, wherein the positive deviation is the current systematic error value minus the upper limit value; Step 363: Normalize the positive deviation to obtain a normalized positive deviation, wherein the normalized positive deviation is the ratio of the positive deviation to the width parameter; Step 364: Substitute the normalized positive deviation into the preset second decay function to calculate the third error effectiveness coefficient.

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