Data consistency calibration method for temperature-pressure composite sensor array

Abstract

The application discloses a data consistency calibration method of a temperature-pressure composite sensor array, and particularly relates to the technical field of data consistency calibration. The method extracts a common calibration curved surface from a full-array pressure response, compresses each node deviation into a low-order individual correction coefficient set, replaces a complete calibration grid with the common curved surface and individual compensation, reduces storage demand by one order of magnitude, estimates slow drift online by using steady-state redundant mutual comparison and low-pass filtering, compensates long-term degradation by only updating the constant term of the correction coefficient, thereby guarantees high consistency of array pressure output in a full temperature-pressure range with minimal storage overhead, and has the self-drift compensation capability without external reference.

Description

Technical Field

[0001] This invention relates to the field of data consistency calibration technology, and more specifically, to a data consistency calibration method for a temperature and pressure composite sensor array. Background Technology

[0002] On platforms such as aircraft and autonomous underwater vehicles, thermo-pressure composite sensor arrays need to provide highly consistent data under varying temperature and pressure environments. Because the output of pressure-sensitive elements drifts significantly with temperature, and the zero points, sensitivity, and temperature characteristics of each node in the array are not identical, engineering practice necessitates two-dimensional calibration of each sensing node across the entire operating temperature and pressure range. This calibration generates corresponding correction surfaces, which are then stored in the non-volatile memory of the acquisition system in the form of coefficient tables or grid data tables for real-time calculation and retrieval.

[0003] However, these embedded platforms are severely constrained by size, power consumption, and cost, resulting in extremely limited non-volatile storage capacity. When the array scales to tens or even hundreds of nodes, the amount of independent, complete calibration grid data for each node rapidly expands, directly exceeding the system's storage limit. Forcibly reducing the calibration grid density to accommodate storage space leads to increased calibration residuals at nodes under combined temperature and pressure conditions, causing the array outputs, which were previously aligned at static single points, to become significantly dispersed again, severely compromising data consistency. The contradiction between storage capacity and array calibration accuracy has become a bottleneck for achieving high-consistency measurements of temperature and pressure composite sensor arrays on embedded platforms. Summary of the Invention

[0004] To overcome the aforementioned deficiencies of the prior art, embodiments of the present invention provide a data consistency calibration method for a temperature and pressure composite sensor array to address the problems mentioned in the background art.

[0005] To achieve the above objectives, the present invention provides the following technical solution: The data consistency calibration method for a temperature and pressure composite sensor array includes the following steps: In a temperature-pressure joint calibration environment, the raw output and standard values ​​of each node in the array are synchronously collected to obtain a two-dimensional response dataset under full operating conditions. The raw output includes raw temperature and pressure outputs, and the standard values ​​include standard temperature and pressure values. Based on the full-condition two-dimensional response dataset, a common calibration surface is extracted with standard temperature and pressure as independent variables and the median envelope of the full array pressure output as a reference, and the polynomial coefficients of the common calibration surface are determined. For each node, calculate the residual between its pressure output and the common calibration surface at the calibration point, and perform low-order surface fitting on the residual to obtain the set of individual deviation correction coefficients for the node; The polynomial coefficients of the common calibration surface and the set of individual deviation correction coefficients of each node are stored in the embedded storage unit to replace the independent complete calibration mesh data of each node. During actual measurement, the original temperature and pressure output of each node are first calculated from the common calibration surface to obtain the reference pressure value, and then the individual deviation correction value obtained by using the individual deviation correction coefficient set of the node is superimposed to obtain the pressure output after consistent calibration. By utilizing the redundant information of the array measuring the same physical field under steady-state conditions, the calibration outputs of each node are compared to estimate the slow drift of the individual deviation correction coefficient set, and the stored individual deviation correction coefficient set is updated with a trend.

[0006] In a preferred embodiment, the step of synchronously acquiring the raw outputs and standard values ​​of each node in the array under a temperature-pressure joint calibration environment to obtain a two-dimensional response dataset under full operating conditions specifically involves: Multiple temperature calibration points are selected within the operating temperature range of the sensor array, and multiple pressure calibration points are selected within the operating pressure range to form calibration operating points; The sensor array is installed in a temperature-pressure combined test chamber, and standard temperature and standard pressure are provided by a standard thermometer and a standard pressure controller, and the pressure interfaces of each node are uniformly connected. For each calibrated operating point, after adjusting the test chamber to the standard temperature and standard pressure and stabilizing, wait for the system to reach thermal equilibrium and pressure steady state, and then synchronously collect the original output of each node and record the standard value. The forward and reverse stroke measurements are performed at all calibrated operating points, and outliers are removed from the collected data to form the full-condition two-dimensional response dataset.

[0007] In a preferred embodiment, the outlier removal of the collected data specifically involves: for each node under each calibration condition, sampling points that deviate from the mean of the node's multiple samplings under the calibration condition by more than three times the standard deviation are removed as outliers, and the average output of the remaining samples after removal is recalculated as the original output value of the node.

[0008] In a preferred embodiment, the step of extracting a common calibration surface based on the full-condition two-dimensional response dataset, using standard temperature and pressure as independent variables and the median envelope of the full array pressure output as a reference, and determining the polynomial coefficients of the common calibration surface, specifically involves: For each calibration operating point, the median value of the original pressure output of all nodes is taken to form a median envelope data point set; The standard temperature and standard pressure are normalized to obtain the normalized temperature and normalized pressure. Using normalized temperature and normalized pressure as independent variables, a bivariate polynomial model is selected. The polynomial coefficients of the common calibration surface are obtained by fitting the median envelope surface data point set using the least squares method. The polynomial order is selected to meet the fitting residual requirements.

[0009] In a preferred embodiment, for each node, the residual between its pressure output and the common calibration surface at the calibration point is calculated, and a low-order surface fitting is performed on the residual to obtain the individual deviation correction coefficient set for the node, specifically: For the i-th node, at each calibration point, the reference pressure value is obtained by using the inverse function of the common calibration surface, based on the original pressure output and standard temperature of the node, and the difference between the reference pressure value and the standard pressure is calculated as the pressure residual. Using the same normalization parameters as the common calibration surface, a low-order polynomial is fitted to the pressure residual with normalized temperature and normalized pressure as independent variables to obtain the set of individual deviation correction coefficients for the node. The order of the low-order polynomial satisfies the requirement that the fitting residual does not exceed a preset proportion of the array's allowable consistency error.

[0010] In a preferred embodiment, storing the polynomial coefficients of the common calibration surface and the set of individual deviation correction coefficients for each node into the embedded storage unit specifically involves: The number of nodes, polynomial order, normalization parameters, polynomial coefficients of the common calibration surface, and individual deviation correction coefficients of each node are arranged in sequence to form a data block. After adding a cyclic redundancy check code, the data is written into the embedded non-volatile memory and then read back for verification after writing.

[0011] In a preferred embodiment, during the actual measurement, the original temperature and pressure outputs of each node are first calculated using the common calibration surface to obtain a reference pressure value, and then the individual deviation correction value obtained using the individual deviation correction coefficient set of the node is superimposed to obtain a uniformly calibrated pressure output, specifically as follows: The node's raw temperature output is converted into a temperature measurement value through a pre-calibrated temperature channel model; By fixing the temperature measurement value, and using the polynomial of the common calibration surface, a reference pressure value that makes the mapping value of the common surface equal to the original pressure output value is obtained through iterative solution. After normalizing the temperature measurement value and the reference pressure value, and substituting them into the individual deviation correction polynomial of the node, the individual deviation correction value is obtained. The calibration pressure output is obtained by adding the reference pressure value to the individual deviation correction value.

[0012] In a preferred embodiment, the redundant information of the array measuring the same physical field under steady-state conditions is used to compare the calibration outputs of each node, estimate the slow drift of the individual deviation correction coefficient set, and perform trend updates on the stored individual deviation correction coefficient set, specifically as follows: During array operation, steady-state conditions are determined based on temperature changes and pressure fluctuations, and when the spatial uniformity of temperature at each node meets the conditions, the current measurement frame is used as an effective steady-state redundant frame. For each effective steady-state redundant frame, the median value of the calibration pressure output of all nodes is taken as the reference pressure, and the deviation between the calibration pressure and the reference pressure of each node is calculated. The deviation is low-pass filtered to obtain a long-term drift estimate; When the absolute value of the long-term drift estimate exceeds the preset tolerance and the preset number of confirmations is met, the constant term in the individual deviation correction coefficient set of the corresponding node is updated with the drift estimate, and the updated individual deviation correction coefficient set is written back to storage.

[0013] In a preferred embodiment, determining the steady-state operating condition based on temperature changes and pressure fluctuations during array operation specifically involves: Within a preset sliding time window, the maximum change in the temperature measurement values ​​of all nodes in the array is lower than the temperature change threshold, and the maximum change in the median value of the array pressure output is lower than the pressure change threshold; the spatial uniformity condition is that the standard deviation of the temperature measurement values ​​of each node is less than the spatial uniformity threshold.

[0014] In a preferred embodiment, writing the updated set of individual deviation correction coefficients back to storage specifically involves: The cyclic redundancy check code is recalculated for the sector data where the node is located, and flash memory erase and write-back operations are performed. If the write-back fails, the backup storage area is activated.

[0015] The technical effects and advantages of this invention are as follows: 1. This invention addresses the problem that large-scale temperature and pressure composite sensor arrays on embedded platforms have extremely limited non-volatile storage capacity, making it impossible to accommodate independent and complete calibration grid data for each node. Forcibly reducing the calibration density leads to increased calibration residuals and disruption of array output consistency under full temperature and pressure conditions. By extracting a common calibration surface from the entire array's pressure response, the deviations of each node are compressed into a set of low-order individual correction coefficients. The complete calibration grid is replaced by a shared surface and individual compensation, reducing storage requirements by an order of magnitude. Furthermore, steady-state redundant cross-comparison and low-pass filtering are used to estimate slow drift online. Only the constant term of the correction coefficients needs to be updated to compensate for long-term degradation. This achieves high consistency of array pressure output across the entire temperature and pressure range with minimal storage overhead and possesses autonomous drift compensation capability without external reference. Attached Figure Description

[0016] To facilitate understanding by those skilled in the art, the present invention will be further described below with reference to the accompanying drawings; Figure 1 This is a flowchart of a method according to an embodiment of the present invention. Detailed Implementation

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

[0018] Example: Figure 1 The present invention provides a data consistency calibration method for a temperature and pressure composite sensor array, comprising the following steps: In a temperature-pressure joint calibration environment, the raw output and standard values ​​of each node in the array are synchronously collected to obtain a two-dimensional response dataset under full operating conditions. The raw output includes raw temperature and pressure outputs, and the standard values ​​include standard temperature and pressure values. Based on the full-condition two-dimensional response dataset, a common calibration surface is extracted with standard temperature and pressure as independent variables and the median envelope of the full array pressure output as a reference, and the polynomial coefficients of the common calibration surface are determined. For each node, calculate the residual between its pressure output and the common calibration surface at the calibration point, and perform low-order surface fitting on the residual to obtain the set of individual deviation correction coefficients for the node; The polynomial coefficients of the common calibration surface and the set of individual deviation correction coefficients of each node are stored in the embedded storage unit to replace the independent complete calibration mesh data of each node. During actual measurement, the original temperature and pressure output of each node are first calculated from the common calibration surface to obtain the reference pressure value, and then the individual deviation correction value obtained by using the individual deviation correction coefficient set of the node is superimposed to obtain the pressure output after consistent calibration. By utilizing the redundant information of the array measuring the same physical field under steady-state conditions, the calibration outputs of each node are compared to estimate the slow drift of the individual deviation correction coefficient set, and the stored individual deviation correction coefficient set is updated with a trend.

[0019] In this embodiment of the invention, the raw outputs and standard values ​​of each node in the array are synchronously acquired in a temperature-pressure joint calibration environment to obtain a two-dimensional response dataset under full operating conditions. The raw outputs include raw temperature and pressure outputs, and the standard values ​​include standard temperature and pressure values, specifically: The operating temperature range is determined based on the expected service environment of the sensor array. and working pressure range In the temperature dimension, K temperature calibration points are selected at non-uniform intervals. This allows the calibration point density in the low-temperature, normal-temperature, and high-temperature regions to adapt to the varying degrees of temperature drift nonlinearity of the sensor. , In terms of pressure, L pressure calibration points are selected. The pressure calibration points include at least the zero pressure point, 25%, 50%, 75% of full scale, and the full scale pressure point, i.e. , This results in K×L calibration operating points on the temperature-pressure plane. Each calibrated operating point represents a combination of standard temperature and standard pressure conditions.

[0020] The sensor array is installed entirely within a temperature-pressure combined test chamber. The chamber contains a standard platinum resistance thermometer and a standard pressure controller. The temperature measurement accuracy of the standard platinum resistance thermometer is more than three times the expected accuracy of each node in the array, and the pressure control accuracy of the standard pressure controller is more than three times the expected accuracy of each node in the array. The standard pressure controller is uniformly connected to the pressure interfaces of all nodes in the array via a pressure manifold to ensure that all nodes experience the standard pressure under the same calibration conditions. Consistent; the standard platinum resistance thermometer is arranged near the geometric center of the array, and its temperature readings are used as the standard temperature. Meanwhile, the spatial non-uniformity of the temperature field is controlled within an allowable range by forced convection or heat transfer medium inside the test chamber.

[0021] Each calibrated working point is checked one by one according to the preset traversal order. Perform steady-state data acquisition: First, adjust the temperature and pressure setpoints of the test chamber to bring the standard temperature and pressure closer to the target values ​​of the current calibration conditions; wait until the standard temperature reaches the target temperature. of Deviation band and standard pressure enters target pressure of After the deviation band, the rate of change of the temperature channel output of each node in the array is continuously monitored. The rate of change is obtained by dividing the difference between the temperature output of two adjacent frames obtained by continuous sampling by the sampling interval; when the rate of change of the temperature output of all nodes is lower than a set threshold... Furthermore, the fluctuation range of the standard pressure is lower than the set threshold. At that time, it is determined that the system has reached sufficient thermal equilibrium and pressure steady state, where It is taken as 3 to 5 times the steady-state noise level of the temperature channel of the sensor array. It is taken as twice the steady-state fluctuation amplitude of the standard pressure controller.

[0022] Once steady state is reached, immediately perform M equally spaced sampling operations on all N nodes of the array, with the sampling interval being... Set the response time to 5-10 times the longer of the sensor's temperature and pressure channels to ensure sufficient temporal decoupling between adjacent samples; record the raw temperature output value of each node in the m-th sample. and the original pressure output value ,in For node indexing, This is the sampling sequence number; simultaneously, the standard temperature value under this calibration condition is recorded. Compared with standard pressure value This refers to the actual measured readings of the standard platinum resistance thermometer and the standard pressure controller at this moment.

[0023] For the M sampled data, the arithmetic mean is calculated node by node to obtain the average raw temperature output of the i-th node under the calibration condition. and average raw pressure output The arithmetic mean is used to suppress random noise in the measurement chain.

[0024] During the process of traversing all K×L calibration operating points, forward stroke measurements are performed in the order of temperature from low to high and pressure from low to high at each constant temperature. Then, reverse stroke measurements are performed in the order of temperature from high to low and pressure from high to low at each constant temperature. Two complete sets of array response data are obtained for forward and reverse stroke measurements, which are used to evaluate the hysteresis characteristics of the sensor nodes.

[0025] After completing the data acquisition for all calibration conditions, outlier removal is performed on the raw data: For each node, the standard deviation of the M sampling sequences under each calibration condition is calculated, and sampling points that deviate from the mean of the sequence by more than ±3 times the standard deviation are identified as outliers and removed. The average raw temperature output and average raw pressure output are recalculated for the remaining valid samples after outlier removal. All valid data retained after outlier removal are summarized to form the array's full-condition two-dimensional response dataset. ; The full-condition two-dimensional response dataset The system fully records the average original temperature output and average original pressure output of each node under all calibrated temperature and pressure combinations, as well as the corresponding standard temperature and standard pressure values, providing a calibration benchmark for the subsequent extraction of the common calibration surface and the set of individual deviation correction coefficients.

[0026] In this embodiment of the invention, based on the full-condition two-dimensional response dataset, a common calibration surface is extracted using standard temperature and pressure as independent variables and the median envelope of the full array pressure output as a reference. The polynomial coefficients of the common calibration surface are then determined, specifically as follows: From the full-condition two-dimensional response dataset Extract the standard temperature corresponding to all K×L calibration operating points. Standard pressure and the average raw pressure output value of each node. For each calibrated operating point, the average raw pressure output values ​​of the N nodes are sorted by numerical value, and the median of the sorted values ​​is taken as the median pressure output value of the array for that operating point. This yields a data point set of the median envelope surface, consisting of the standard temperature, standard pressure, and median pressure output values ​​of all calibrated operating points. The median envelope surface eliminates the influence of individual extreme deviation nodes under each calibration condition, representing the common trend of array pressure response.

[0027] A bivariate polynomial model is selected as the functional form of the common calibration surface, and its expression is: In order to reduce the condition number of the regularization equation caused by the scale difference of the independent variables, the standard temperature and standard pressure are linearly normalized, and the normalized temperature is set to... Normalization pressure , , , and Defined in the same way; , , where m and n are the polynomial orders in the temperature and pressure directions, respectively; denoted as the coefficients of the polynomial to be determined.

[0028] Each data point in the median envelope data point set M Mapping to normalized independent variables , With dependent variable Construct a polynomial coefficient For an overdetermined system of linear equations, solve for the coefficient vector using the least squares method. This makes the sum of squared residuals Minimize. The polynomial order m and n are determined based on the measured temperature drift nonlinearity of the pressure channel of the sensor array. Under the premise that the root mean square of the fitting residual is not greater than 0.05% of the full-scale output, the order combination that minimizes the total number of coefficients (m+1)×(n+1) is selected.

[0029] The set of polynomial coefficients obtained from the solution With normalized parameters , , , Also recorded is that the set of polynomial coefficients and the normalization parameters together define the common calibration surface, which describes the common response relationship of the entire array pressure output relative to standard temperature and standard pressure, and serves as the benchmark for subsequent individual deviation correction of each node.

[0030] In this embodiment of the invention, for each node, the residual between its pressure output and the common calibration surface at the calibration point is calculated. A low-order surface fitting is performed on the residual to obtain the individual deviation correction coefficient set for the node, specifically: From the full-condition two-dimensional response dataset Extract the average raw pressure output value of the i-th node under all calibrated operating conditions. Standard temperature Compared with standard pressure Where i=1,…,N; based on the established common calibration surface, this surface provides a mapping relationship from standard temperature and standard pressure to the original pressure output at the center of the array. Its polynomial coefficient set With normalized parameters , , , Known.

[0031] For each calibration point of the i-th node The reference pressure value of the node is calculated using the inverse function of the common calibration surface. The reference pressure value satisfies the equation At a fixed temperature Under the condition that the function Since the pressure P is strictly monotonic within the working pressure range, the solution to the above equation exists and is unique; a bisection method is used for iterative solution: a pressure search interval is defined. Take the midpoint of the interval ,calculate If less than If the lower bound is not updated to the midpoint, then the upper bound is updated to the midpoint; otherwise, the upper bound is updated to the midpoint. This process is repeated until the interval width is less than the full-scale pressure. The midpoint of this interval is the required baseline pressure value. .

[0032] After obtaining the reference pressure value at the calibration point, calculate the pressure residual corresponding to the nodal pressure output at that point. ; The pressure residual represents the systematic deviation of the calculated value of node i relative to the standard pressure if the pressure is directly solved using the inverse function of the array's common calibration surface; the distribution of this deviation across the entire temperature and pressure range reflects the individual differences between the node and the array's common response.

[0033] To describe this individual variability in a compact form, a low-order surface fit is performed on the pressure residuals on the temperature-pressure plane. Using the same normalization parameters as the common calibration surface, standard temperature and standard pressure are mapped as normalized independent variables. , A low-order bivariate polynomial model is selected as the functional form of the individual deviation correction surface, and its expression is: Where r and s are the orders in the temperature and pressure directions, respectively, and we take... , Furthermore, the total number of terms is much smaller than the number of terms on the common calibration surface; Let be the individual deviation correction coefficient for the i-th node to be determined.

[0034] With all calibration point data Construct an overdetermined system of equations and solve for the coefficient vector using the least squares method. This makes the sum of squared residuals Minimize; the selection of order r and s is based on the criterion that the maximum value of the fitting residual at each calibration point does not exceed 1 / 3 of the array’s allowable consistency error, and lower order is preferred to limit storage overhead.

[0035] The individual bias correction coefficient obtained by solving With normalized parameters , , , Together, they constitute the individual deviation correction coefficient set for the i-th node. This coefficient set, with a small number of parameters, characterizes the low-order variation trend of the node's individual deviation across the entire operating temperature and pressure range. In embedded applications, only storage is required. A single floating-point number is enough to reproduce the complete deviation correction surface.

[0036] In this embodiment of the invention, the polynomial coefficients of the common calibration surface and the set of individual deviation correction coefficients for each node are stored in an embedded storage unit to replace the independent complete calibration mesh data for each node. Specifically: Based on the polynomial orders m and n of the determined common calibration surface, the polynomial orders r and s of the individual deviation correction surfaces of each node, and the total number of nodes N of the sensor array, the total number of floating-point coefficients required to be stored for this calibration method is calculated. ,in To store normalization parameters , , , The number of floating-point numbers required, take Simultaneously calculate the total number of floating-point numbers required to store a two-dimensional lookup table for each node when using independently complete calibration grid data. K and L represent the number of calibration points in the temperature and pressure directions, respectively, with a typical array size of N=64, calibration grid K=11, L=11, and common surface order. Correcting the order of the surface For example, A floating-point number, approximately equal to (Based on single-precision 4-byte units), while Each floating-point number, approximately 2.33 KB, reduces storage requirements by an order of magnitude, allowing all array calibration coefficients to be fully accommodated in the on-chip flash memory of the embedded microcontroller without the need for external memory expansion.

[0037] The data to be stored is organized into contiguous data blocks according to a preset binary storage layout. The header area of ​​each data block is sequentially written with the total number of nodes N, the order of the common surface m and n, the order of the modified surface r and s, and the normalization parameter. , , , Then, the coefficients of the common calibration surface polynomial are written in row-major order. Then, according to the node numbers i=1 to N, the individual deviation correction coefficient set for each node is written in sequence. All multi-byte floating-point numbers are stored in little-endian byte order according to the IEEE 754 single-precision format to ensure consistent parsing across platforms.

[0038] A Cyclic Redundancy Check (CRC-32) code is calculated for the continuous data blocks, and the check code is appended to the end of the data blocks to form a complete storage image with check information. The storage image is written to the non-volatile storage unit by page erasure and page programming through the flash programming interface of the embedded microcontroller. During the writing process, all physical pages in the target address range are erased first, and then the storage image is divided into pages according to the page size and written page by page. After each page is written, a readback check is performed to confirm that the readback data is consistent with the content of the write buffer byte by byte. If the readback fails, the page is rewritten once. If the rewrite still fails, the storage area is marked as abnormal and the backup storage area is enabled.

[0039] After all data is written, the header area is reread from the flash memory to parse out N, m, n, r, s, and the normalized parameters. All coefficients are then read sequentially, and the stored CRC checksum is used to verify the integrity of the entire data block. Upon successful verification, the normalized parameters, the polynomial coefficients of the common calibration surface, and the set of individual deviation correction coefficients for each node are loaded into the calibration parameter structure in the microcontroller's memory for real-time measurement and calculation. Thus, the compressed calibration data composed of the common calibration surface and the set of individual deviation correction coefficients completely replaces the independent complete calibration grid data for each node. This solves the problem of large-scale array calibration data exceeding the non-volatile storage capacity of the embedded system while ensuring the accuracy of full temperature and pressure calibration.

[0040] In this embodiment of the invention, during actual measurement, the original temperature and pressure output of each node are first calculated using the common calibration surface to obtain a reference pressure value, and then the individual deviation correction value obtained using the individual deviation correction coefficient set of the node is superimposed to obtain a pressure output after consistent calibration. Specifically: During each measurement cycle of the embedded microcontroller, the raw temperature output value of the i-th node in the array is synchronously acquired. and the original pressure output value Where i=1,…,N; First, the temperature channel calibration model established by this node during the calibration phase is utilized. Convert the raw temperature output into a temperature measurement value. The temperature channel calibration model is a cubic polynomial. Its coefficient During the calibration phase, the standard temperature and the original temperature output value of the node at each temperature calibration point are determined by least squares fitting, and stored together with the set of individual deviation correction coefficients in the embedded storage unit.

[0041] Call the stored set of polynomial coefficients of the common calibration surface With normalized parameters , , , Construct a positive mapping function for the common calibration surface. ,in , Let be the normalized pressure variable to be solved. Let be the output from the original pressure. Inversely calculate the reference pressure value and establish the equation. At a fixed normalization temperature Under the condition that the common calibration surface is polynomial in the pressure dimension about The normalized pressure is continuous and strictly monotonically increasing within the normalized pressure interval [−1, 1], therefore the above equation has a unique solution; a bisection method is used for iterative solution: a normalized pressure search interval is set. Calculate the midpoint of the interval function value at ,like If the lower bound is not updated to the midpoint, then the upper bound is updated to the midpoint; otherwise, the upper bound is updated to the midpoint. This process is repeated until the interval width is less than the full-scale pressure. Multiply by 1, and take the midpoint of the final interval. The normalized reference pressure value is then denormalized to obtain the reference pressure value. .

[0042] Call the stored set of individual deviation correction coefficients for the i-th node Using normalized parameters, calculate the individual deviation correction value for this node under the current temperature and pressure conditions. (The temperature measurement value is then used.) Compared with the reference pressure value Mapped to normalized independent variables using the same normalization parameters. , Substitute the polynomial expression of the individual deviation correction surface The individual bias correction value was calculated. This correction value represents the amount of system deviation compensation for node i relative to the array common response under the current operating conditions.

[0043] The reference pressure value is added to the individual deviation correction value to obtain the pressure output value after consistent calibration. The This represents the final pressure measurement result of the i-th node after full array consistency calibration. The above calculation process is repeated for all N nodes in the array to obtain the consistent calibrated pressure output value for each node. The maximum deviation between the pressure outputs of each node across the entire temperature and pressure range is determined by the common fitting residual of the common calibration surface and the correction residual of the individual deviation correction surface, and the maximum deviation is constrained within the allowable consistency error range of the array.

[0044] In this embodiment of the invention, redundant information from the array measuring the same physical field under steady-state conditions is utilized to compare the calibration outputs of each node, estimate the slow drift of the individual deviation correction coefficient set, and perform trend updates on the stored individual deviation correction coefficient set, specifically as follows: During continuous online operation of the sensor array, the embedded microcontroller synchronously obtains the consistent calibrated pressure output values ​​of each node in each measurement cycle. With temperature measurement value Where i=1,…,N. First, determine whether the current condition is steady-state based on the time-varying characteristics of temperature and pressure: continuously monitor the maximum change in temperature measurements of all nodes in the array within a sliding time window W (W=60 seconds). and the median value of array pressure output Maximum change within the same window When both conditions are met and When the system is deemed to have entered a steady-state condition, the threshold value is determined. Set to 3 times the array temperature noise level. Set to 3 times the array pressure noise level. To ensure that all nodes in the array are indeed measuring the same physical field, further check the spatial uniformity of the temperature field: calculate the standard deviation of the temperature measurements at each node at this moment. ,Require , The temperature difference consistency index allowed by the sensor array is set, for example, 0.1°C. When all the above conditions are met, the current measurement frame is considered a valid steady-state redundant frame.

[0045] For each valid steady-state redundant frame, the reference pressure value is constructed using the calibration pressure output of all array nodes at that moment as input and the median method. The median, instead of the mean, is used to suppress the influence of individual nodes that have experienced significant faults or drift on the reference value. For the i-th node, the pressure deviation in the current frame is calculated. ; The deviation This refers to the instantaneous inconsistency error of the node relative to the common reference of the array under the current operating conditions.

[0046] To separate the systematic bias caused by the slow drift of the sensor from the instantaneous deviation, a first-order low-pass filter is maintained for each node, with the recursive form as follows: ,in The filtered long-term deviation estimate is given at the initialization time. α is the filter coefficient. Taking α=0.01 corresponds to a time constant of approximately 100 steady-state frames, which allows the filter to track only slow drift processes with a change period much larger than thermal transients and turbulent fluctuations.

[0047] When the filtered output of H consecutive effective steady-state redundant frames Exceeding the allowable drift tolerance At that time, that is If the duration exceeds the confirmation window H (H=20), then the trend update of the individual deviation correction coefficient set is initiated. Considering that the deviation of the correction surface determined in a single calibration cycle is mainly reflected in the overall offset in the pressure direction after long-term service, the offset can be equivalent to the constant term in the polynomial of the individual deviation correction surface. The increment, because from the correction formula It can be seen that when , When, the correction value is This directly contributes a fixed pressure bias that is independent of the operating condition. Therefore, the estimated slow drift is... .

[0048] After the update is triggered, the set of individual deviation correction coefficients for the i-th node stored in the non-volatile memory unit is modified online: the original coefficients are read. Calculate the updated value , will the new constant term Replace the original value, keeping the other coefficients. Remaining unchanged, forming the updated set of individual bias correction coefficients. Subsequently, the data blocks are repackaged in the same format as in the initial storage phase, the cyclic redundancy check (CRC-32) code is recalculated for the data in the sector where the node resides, and flash erase and write-back operations are performed to complete the in-situ update of the non-volatile memory cells. After a successful update, the long-term deviation from the estimate will be recorded. Reset to 0 to avoid repeated accumulation.

[0049] Through the aforementioned online cross-comparison and trend update mechanism, the array can autonomously perceive the individual drift of each node during long-term operation and track the slow changes in the correction coefficient set with extremely low computational and storage overhead, enabling the array to maintain high consistency without the need for laboratory recalibration.

[0050] This invention extracts a common calibration surface from the full array pressure output and describes the common temperature-pressure response of the array using a single polynomial coefficient set. It compresses the complete two-dimensional calibration mesh data of each node into a shared common surface coefficient set and a set of low-order individual deviation correction coefficients unique to each node. This reduces the total storage of calibration parameters for large-scale arrays by an order of magnitude, allowing them to be directly housed in the on-chip flash memory of an embedded microcontroller. This preserves the full temperature-pressure calibration information within limited non-volatile storage resources, avoiding the amplification of calibration residuals and array output dispersion introduced by forcibly reducing the calibration mesh density. Simultaneously, using the median envelope of the full array pressure output as the fitting benchmark for the common calibration surface naturally suppresses interference from individual abnormal nodes when extracting the common response. This ensures the common surface robustly reflects the main characteristics of the array, reducing the amplitude of individual deviation residuals at each node. This, in turn, allows for accurate fitting of the deviation correction surface using low-order polynomials and further reduces the storage overhead of individual correction coefficients. By comparing the calibration outputs of each node under steady-state conditions using redundant information from array measurements of the same physical field, and estimating the slow drift using the median reference value and first-order low-pass filtering, long-term drift can be compensated by simply updating the constant terms in the individual deviation correction coefficient set. The entire online compensation process has extremely low computational cost and requires no external standard source, enabling the array to maintain high consistency autonomously during long-term operation on the embedded platform, thus overcoming the problem of gradual inaccuracy caused by node individualization degradation.

[0051] This invention addresses the problem that large-scale temperature and pressure composite sensor arrays on embedded platforms have extremely limited non-volatile storage capacity, making it impossible to accommodate independent and complete calibration grid data for each node. Forcibly reducing the calibration density leads to increased calibration residuals and disruption of array output consistency under full temperature and pressure conditions. By extracting a common calibration surface from the entire array's pressure response, the deviations of each node are compressed into a set of low-order individual correction coefficients. The complete calibration grid is replaced by a shared surface plus individual compensation, reducing storage requirements by an order of magnitude. Furthermore, steady-state redundant cross-comparison and low-pass filtering are used to estimate slow drift online. Only the constant term of the correction coefficients needs to be updated to compensate for long-term degradation. This achieves high consistency of array pressure output across the entire temperature and pressure range with minimal storage overhead and possesses autonomous drift compensation capability without external reference.

[0052] The above formulas are all dimensionless calculations. The formulas are derived from software simulations based on a large amount of collected data to obtain the most recent real-world results. The preset parameters in the formulas are set by those skilled in the art according to the actual situation.

[0053] It should be understood that in the various embodiments of this application, the order of the above-mentioned processes does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of this application.

[0054] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A data consistency calibration method for a temperature and pressure composite sensor array, characterized in that: The steps include the following: In a temperature-pressure joint calibration environment, the raw output and standard values ​​of each node in the array are synchronously collected to obtain a two-dimensional response dataset under full operating conditions. The raw output includes raw temperature and pressure outputs, and the standard values ​​include standard temperature and pressure values. Based on the full-condition two-dimensional response dataset, a common calibration surface is extracted with standard temperature and pressure as independent variables and the median envelope of the full array pressure output as a reference, and the polynomial coefficients of the common calibration surface are determined. For each node, calculate the residual between its pressure output and the common calibration surface at the calibration point, and perform low-order surface fitting on the residual to obtain the set of individual deviation correction coefficients for the node; The polynomial coefficients of the common calibration surface and the set of individual deviation correction coefficients of each node are stored in the embedded storage unit to replace the independent complete calibration mesh data of each node. During actual measurement, the original temperature and pressure output of each node are first calculated from the common calibration surface to obtain the reference pressure value, and then the individual deviation correction value obtained by using the individual deviation correction coefficient set of the node is superimposed to obtain the pressure output after consistent calibration. By utilizing the redundant information of the array measuring the same physical field under steady-state conditions, the calibration outputs of each node are compared to estimate the slow drift of the individual deviation correction coefficient set, and the stored individual deviation correction coefficient set is updated with a trend.

2. The data consistency calibration method for a temperature and pressure composite sensor array according to claim 1, characterized in that: The process of synchronously acquiring the raw outputs and standard values ​​of each node in the array within a temperature-pressure joint calibration environment to obtain a two-dimensional response dataset under full operating conditions is specifically as follows: Multiple temperature calibration points are selected within the operating temperature range of the sensor array, and multiple pressure calibration points are selected within the operating pressure range to form calibration operating points; The sensor array is installed in a temperature-pressure combined test chamber, and standard temperature and standard pressure are provided by a standard thermometer and a standard pressure controller, and the pressure interfaces of each node are uniformly connected. For each calibrated operating point, after adjusting the test chamber to the standard temperature and standard pressure and stabilizing, wait for the system to reach thermal equilibrium and pressure steady state, and then synchronously collect the original output of each node and record the standard value. The forward and reverse stroke measurements are performed at all calibrated operating points, and outliers are removed from the collected data to form the full-condition two-dimensional response dataset.

3. The data consistency calibration method for a temperature and pressure composite sensor array according to claim 2, characterized in that: The outlier removal process for the collected data is as follows: for each node under each calibration condition, sampling points that deviate from the mean of the node's multiple samplings under the calibration condition by more than three times the standard deviation are removed as outliers. The average output of the remaining samples after removal is then recalculated and used as the original output value of the node.

4. The data consistency calibration method for a temperature and pressure composite sensor array according to claim 1, characterized in that: The step involves extracting a common calibration surface based on the full-condition two-dimensional response dataset, using standard temperature and pressure as independent variables and the median envelope of the full array pressure output as a reference, and determining the polynomial coefficients of the common calibration surface. Specifically: For each calibration operating point, the median value of the original pressure output of all nodes is taken to form a median envelope data point set; The standard temperature and standard pressure are normalized to obtain the normalized temperature and normalized pressure. Using normalized temperature and normalized pressure as independent variables, a bivariate polynomial model is selected. The polynomial coefficients of the common calibration surface are obtained by fitting the median envelope surface data point set using the least squares method. The polynomial order is selected to meet the fitting residual requirements.

5. The data consistency calibration method for a temperature and pressure composite sensor array according to claim 1, characterized in that: For each node, the residual between its pressure output and the common calibration surface at the calibration point is calculated. A low-order surface fitting is then performed on the residual to obtain the individual deviation correction coefficient set for the node. Specifically: For the i-th node, at each calibration point, the reference pressure value is obtained by using the inverse function of the common calibration surface, based on the original pressure output and standard temperature of the node, and the difference between the reference pressure value and the standard pressure is calculated as the pressure residual. Using the same normalization parameters as the common calibration surface, a low-order polynomial is fitted to the pressure residual with normalized temperature and normalized pressure as independent variables to obtain the set of individual deviation correction coefficients for the node. The order of the low-order polynomial satisfies the requirement that the fitting residual does not exceed a preset proportion of the array's allowable consistency error.

6. The data consistency calibration method for a temperature and pressure composite sensor array according to claim 1, characterized in that: The step of storing the polynomial coefficients of the common calibration surface and the set of individual deviation correction coefficients for each node into the embedded storage unit specifically involves: The number of nodes, polynomial order, normalization parameters, polynomial coefficients of the common calibration surface, and individual deviation correction coefficients of each node are arranged in sequence to form a data block. After adding a cyclic redundancy check code, the data is written into the embedded non-volatile memory and then read back for verification after writing.

7. The data consistency calibration method for a temperature and pressure composite sensor array according to claim 1, characterized in that: During the actual measurement, the original temperature and pressure outputs of each node are first calculated using the common calibration surface to obtain a reference pressure value. Then, the individual deviation correction values ​​obtained using the individual deviation correction coefficient set of the node are superimposed to obtain a consistent calibrated pressure output. Specifically: The node's raw temperature output is converted into a temperature measurement value through a pre-calibrated temperature channel model; By fixing the temperature measurement value, and using the polynomial of the common calibration surface, a reference pressure value that makes the mapping value of the common surface equal to the original pressure output value is obtained through iterative solution. After normalizing the temperature measurement value and the reference pressure value, and substituting them into the individual deviation correction polynomial of the node, the individual deviation correction value is obtained. The calibration pressure output is obtained by adding the reference pressure value to the individual deviation correction value.

8. The data consistency calibration method for a temperature and pressure composite sensor array according to claim 1, characterized in that: The method involves utilizing redundant information from the array's measurements of the same physical field under steady-state conditions, comparing the calibration outputs of each node, estimating the slow drift of the individual deviation correction coefficient set, and updating the stored individual deviation correction coefficient set according to its trend. Specifically: During array operation, steady-state conditions are determined based on temperature changes and pressure fluctuations, and when the spatial uniformity of temperature at each node meets the conditions, the current measurement frame is used as an effective steady-state redundant frame. For each effective steady-state redundant frame, the median value of the calibration pressure output of all nodes is taken as the reference pressure, and the deviation between the calibration pressure and the reference pressure of each node is calculated. The deviation is low-pass filtered to obtain a long-term drift estimate; When the absolute value of the long-term drift estimate exceeds the preset tolerance and the preset number of confirmations is met, the constant term in the individual deviation correction coefficient set of the corresponding node is updated with the drift estimate, and the updated individual deviation correction coefficient set is written back to storage.

9. The data consistency calibration method for a temperature and pressure composite sensor array according to claim 8, characterized in that: The steady-state operating condition is determined based on temperature changes and pressure fluctuations during array operation, specifically as follows: Within a preset sliding time window, the maximum change in the temperature measurement values ​​of all nodes in the array is lower than the temperature change threshold, and the maximum change in the median value of the array pressure output is lower than the pressure change threshold; the spatial uniformity condition is that the standard deviation of the temperature measurement values ​​of each node is less than the spatial uniformity threshold.

10. The data consistency calibration method for a temperature and pressure composite sensor array according to claim 8, characterized in that: The step of writing the updated set of individual deviation correction coefficients back to storage specifically involves: The cyclic redundancy check code is recalculated for the sector data where the node is located, and flash memory erase and write-back operations are performed. If the write-back fails, the backup storage area is activated.

Images