An all-fiber voltage transformer temperature compensation measurement method and device

Abstract

The application discloses a kind of all-fiber voltage transformer temperature compensation measurement method and device, through the joint screening of multiple measuring points phase and temperature data, stable phase reference is determined by excluding self-heating interference;Through the separation of heating and cooling path and the point-by-point time shift correction combined with the response lag characteristics of each measuring point, the complete law of phase change with temperature is described, and the temperature drift curve is formed;Using partition weighted fitting and cross-measuring point consistency verification, the temperature coefficient that fits the difference characteristics of each measuring point is obtained;Further track the change trend of hysteresis width under multiple thermal cycles, and generate graded compensation basis by reverse calculation combined with temperature coefficient;Finally, according to the compensation parameters and response rate adaptation, the transient error is dynamically calculated during temperature jump process and is superimposed with steady-state compensation output, forming a compensation measurement result that takes into account steady-state and transient error, which can provide support for stable measurement of all-fiber voltage transformer in complex temperature environment.

Description

Technical Field

[0001] This invention relates to the field of temperature compensation measurement technology for power equipment, and in particular to a method and apparatus for temperature compensation measurement of an all-fiber voltage transformer. Background Technology

[0002] All-fiber voltage transformers measure high-voltage side electrical signals using fiber optic sensing principles. They offer advantages such as good insulation performance, strong resistance to electromagnetic interference, and ease of integration with digital systems, making them widely used in power system voltage measurement. However, the fiber optic sensing elements and supporting optics relied upon by these transformers are highly sensitive to changes in ambient temperature. Temperature fluctuations can cause phase shifts in the optical path, thus affecting the accuracy of voltage measurement results. Temperature-induced measurement errors have become a significant factor limiting further improvements in the measurement accuracy of all-fiber voltage transformers.

[0003] Existing temperature compensation methods mostly rely on a single measuring point or a fixed temperature coefficient for correction, without fully considering the differences in the response of multiple measuring points inside the sensor head. They also fail to accurately reflect the asymmetric change patterns that occur during repeated temperature rises and falls. Furthermore, they lack targeted methods for handling dynamic errors when the temperature changes abruptly, resulting in deviations in compensation results in extreme temperature ranges and scenarios with drastic temperature fluctuations. This makes it difficult to meet the high-precision measurement requirements of all-fiber voltage transformers in complex operating environments. Summary of the Invention

[0004] This invention discloses a temperature compensation measurement method and device for all-fiber voltage transformers, aiming to establish a stable and reliable phase reference, characterize the phase drift law caused by temperature changes, determine the temperature coefficient of each measurement point by combining partition fitting, and generate a graded compensation basis by tracking the hysteresis change trend under multiple thermal cycles. At the same time, it takes into account the dynamic response during the sudden temperature change process, and realizes comprehensive compensation for the measurement error of all-fiber voltage transformers, providing more accurate and reliable voltage measurement data for applications such as power grid voltage monitoring and relay protection.

[0005] The first aspect of this invention proposes a method for measuring temperature compensation in an all-fiber voltage transformer, comprising the following steps:

[0006] Collect phase waveforms and temperature distribution arrays from multiple measurement points, and use the phase waveforms and temperature distribution arrays to identify self-heating saturation, eliminate stable sections, and determine the reference phase value.

[0007] Based on the phase waveform and the reference phase value, the heating and cooling paths are separated to determine the phase offset segment. The phase offset segment and the temperature distribution array are mapped to form a temperature drift rate curve. The temperature drift rate curve is used to perform hysteresis decoupling to construct the temperature drift curve.

[0008] The high-slope continuous section of the temperature drift curve is retained to generate candidate intervals for coefficients. Based on the candidate intervals for coefficients and the reference phase value, the extreme temperature region is weighted and calculated to obtain the initial temperature coefficient value group. The initial temperature coefficient value group is then corrected by cross-measuring point consistency verification and output as a temperature coefficient matrix.

[0009] Based on the phase offset segment, the temperature drift hysteresis curve is obtained by identifying the growth trend of the hysteresis width of multiple thermal cycles. The hysteresis width is then calibrated in reverse using the temperature drift hysteresis curve and the temperature coefficient matrix to generate error compensation levels. Based on the error compensation levels, the compensation values ​​of adjacent levels are weighted and verified to output a graded compensation strategy.

[0010] Based on the graded compensation strategy, a compensation parameter table is constructed by setting the density distribution. The response rate adaptability is verified through the compensation parameter table to determine the corrected response weight. Based on the compensation parameter table and the corrected response weight, the jump response from room temperature to extreme temperature is verified to obtain the voltage measurement result after compensation.

[0011] A second aspect of the present invention provides a temperature compensation measuring device for an all-fiber voltage transformer, comprising:

[0012] The phase acquisition module is used to acquire phase waveforms and temperature distribution arrays at multiple measurement points, and to identify self-heating saturation and eliminate stable sections based on the phase waveforms and temperature distribution arrays to determine the reference phase value.

[0013] The path decoupling module is used to separate the heating and cooling paths based on the phase waveform and the reference phase value to determine the phase offset segment, form a temperature drift rate curve by mapping the phase offset segment and the temperature distribution array rate ratio, and use the temperature drift rate curve to perform lag time descending order decoupling to construct the temperature drift curve.

[0014] The coefficient calibration module is used to generate candidate intervals for coefficients by retaining the high-slope continuous section of the temperature drift curve, calculate the extreme temperature range based on the candidate intervals and the reference phase value to obtain the initial temperature coefficient value group, and perform cross-measuring point consistency verification and correction on the initial temperature coefficient value group to output the temperature coefficient matrix.

[0015] The gear calibration module is used to identify the increasing trend of hysteresis width in multiple thermal cycles based on the phase offset segment to obtain the temperature drift hysteresis curve. The hysteresis width is calibrated in reverse by the temperature drift hysteresis curve and the temperature coefficient matrix to generate the error compensation gear. The error compensation gear is used to weight and verify the compensation values ​​of adjacent gears and output a graded compensation strategy.

[0016] The compensation output module is used to construct a compensation parameter table based on the density distribution setting of the hierarchical compensation strategy, determine the corrected response weight by verifying the response rate adaptability through the compensation parameter table, and obtain the compensated voltage measurement result by verifying the jump response from room temperature to extreme temperature based on the compensation parameter table and the corrected response weight.

[0017] The beneficial effects of this invention are reflected in the following points: First, this invention does not rely on a single measuring point or an instantaneous reading after a single power-on to determine the phase starting point. Instead, it determines the benchmark by screening the phase and temperature data of multiple measuring points layer by layer, eliminating interference from the stage before self-heating saturation, thus ensuring the stability of the benchmark across power-on cycles. Based on this, it separates the heating and cooling paths and performs time-shifting and connection correction point by point to address the inherent response lag of each measuring point. This realigns the phase data of multiple measuring points, which were originally misaligned due to lag, to the same time benchmark, providing a common starting point that closely reflects the actual state of the equipment for subsequent compensation work. Second, addressing the inconsistency of the temperature coefficient across low, high, and normal temperature ranges, this invention does not use a uniform coefficient covering the entire temperature range. Instead, it first divides different temperature zones, allocates fitting weights differently according to the degree of deviation of each temperature zone from the benchmark, performs fitting point by point, and performs cross-point verification and correction for measuring point results with significant deviations. This ensures that the final temperature coefficient reflects the inherent differences between different measuring points and avoids interference from abnormal readings of individual measuring points on the overall compensation basis. Finally, this invention focuses on the gradual change of hysteresis width with the progression of thermal cycling. To this end, its evolution curve is established and extrapolated according to the growth rate. Combined with the temperature coefficient, the basis for graded compensation is calculated in reverse, which makes up for the shortcomings of previous schemes that ignored the cumulative effect of thermal cycling. The compensation parameter table takes into account both the steady-state temperature drift main term and the hysteresis additional deviation, and conducts jump response verification for sudden temperature change conditions. The transient error is dynamically calculated and superimposed with the steady-state compensation, taking into account both normal and extreme conditions with drastic temperature fluctuations. Attached Figure Description

[0018] Figure 1 This is a flowchart illustrating a method for measuring temperature compensation in an all-fiber voltage transformer according to the present invention.

[0019] Figure 2 This is a schematic diagram of the multi-point hysteresis decoupling and temperature drift curve splicing of the present invention.

[0020] Figure 3 This is a structural block diagram of a temperature compensation measurement device for an all-fiber voltage transformer according to the present invention.

[0021] Where: 1-represents lag time; 2-processing order; 3-reverse time shift; 4-connection correction amount; 5-reference value update direction; 6-point-by-point correction curve; 7-time alignment line; 8-temperature drift curve. Detailed Implementation

[0022] In the following description, specific details such as particular system architectures and techniques are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of this application. However, those skilled in the art will understand that this application may also be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods have been omitted so as not to obscure the description of this application with unnecessary detail.

[0023] References to "one embodiment" or "some embodiments" as described in this specification mean that one or more embodiments of this application include a specific feature, structure, or characteristic described in connection with that embodiment. Therefore, the phrases "in one embodiment," "in some embodiments," "in other embodiments," "in still other embodiments," etc., appearing in different parts of this specification do not necessarily refer to the same embodiment, but rather mean "one or more, but not all, embodiments," unless otherwise specifically emphasized. The terms "comprising," "including," "having," and variations thereof mean "including but not limited to," unless otherwise specifically emphasized.

[0024] The technical solutions of the embodiments of this application will be described below.

[0025] like Figure 1 As shown, this embodiment of the invention provides a method for measuring temperature compensation of an all-fiber voltage transformer, including the following steps S101-S105:

[0026] Step S101: Collect phase waveforms and temperature distribution arrays from multiple measurement points, and determine the reference phase value by identifying self-heating saturation and excluding stable sections based on the phase waveforms and temperature distribution arrays.

[0027] Specifically, phase waveforms and temperature distribution arrays at multiple measurement points are acquired. A sensing fiber is wound around the surface of a high-voltage piezoelectric element within the sensing head. Six measurement points are set along this fiber, each corresponding to an independent interferometric demodulation channel and a surface-mount fiber Bragg grating thermometer. These are wound together with the sensing fiber and integrated into the sensing head within a cavity filled with potting compound, with their physical positions corresponding one-to-one. A narrow-linewidth laser is branched into the interferometric loop at each measurement point via a 1×6 fiber coupler. A phase modulator within the loop applies sinusoidal carrier modulation. The intensity modulation signal at each measurement point is synchronously acquired by a photodetector at a sampling rate of 10kHz. After analog-to-digital conversion, the signal is sent to a field-programmable gate array (FPGA) and demodulated point-by-point using a phase-carrier generation algorithm. The calculated phase waveforms are recorded in radians in chronological order of sampling time. The phase waveforms of the six measurement points are stored side-by-side in the same time slice according to the measurement point number. The temperature measurement channel and the phase measurement channel share the same clock source for triggering acquisition. The reflected wavelength of the fiber optic grating is obtained by scanning with a spectrometer demodulator. The nominal resolution of the converted temperature value is 0.01℃. The scanning period is 100 milliseconds, which is 1000 times the phase sampling period. The temperature values ​​of each measurement point are arranged according to the measurement point number and written into the temperature distribution array. The phase sampling time between two scans uses the temperature value obtained from the previous scan, so that the temperature values ​​in the temperature distribution array are aligned with the phase waveforms in the same time slice. Each row of the temperature distribution array corresponds to a sampling time, and each column corresponds to a measurement point. The row and column structure is consistent with the phase waveform, and the timestamp is generated by the gate array clock counter. After the device is powered on, the light source and demodulation circuit continuously dissipate heat. The heat is transferred through the encapsulation structure, causing the temperature of each measurement point to rise on its own even when the ambient temperature remains constant. This process is called self-heating. The phase change caused by self-heating and the external temperature is superimposed on the waveform and cannot be directly distinguished. Therefore, the reference phase value must be determined after the self-heating saturates.

[0028] In some embodiments, the step of identifying self-heating saturation and excluding stable sections based on the phase waveform and the temperature distribution array to determine the reference phase value includes: performing time-by-time stability scanning on the phase waveform to obtain candidate stable time periods; performing temperature synchronization verification based on the candidate stable time periods and the temperature distribution array to obtain environmental stable time periods; performing phase mean statistics to eliminate the largest deviation measurement points through the environmental stable time periods to obtain a reference phase value; and performing inter-measurement deviation verification on the reference phase value to determine the reference phase value.

[0029] Candidate stationary periods are obtained by performing a time-by-time stationarity scan on the phase waveform. The scan window is 2 seconds long with a step size of 0.5 seconds, and adjacent windows overlap by 75%. At a sampling rate of 10kHz, one window accommodates 20,000 raw sampling points, and one forward shift is equivalent to a displacement of 5,000 points, which is accomplished by the shift register in the gate array. The six measurement point channels share the same sliding window logic, each maintaining independent start and end pointers. The standard deviation of the phase waveform within each window is calculated point by point using the raw sampling values ​​of all six measurement points. The calculation method is to calculate the difference between each point and the window mean, square it, accumulate the results, divide by the number of sampling points, and then take the square root. The smaller the value, the closer the phase waveform within the window is to stationarity. The scan window is marked as valid when its standard deviation is lower than a set threshold. The threshold is three times the statistical value of the phase standard deviation obtained by the sensor head after self-heating saturation in a constant temperature environment for 20 minutes, representing the upper limit of the device's own noise level. The standard deviation of all six measurement points must be lower than the threshold simultaneously for the window to be considered valid. The standard deviation is calculated window by window along the time axis, and the scan continues until the end of the data acquisition. Multiple consecutive valid windows are joined end-to-end and merged into a continuous time interval. Only merged intervals lasting at least 1 minute are recorded as candidate stationary time periods, including start and end timestamps. Merged intervals less than 1 minute are not recorded to ensure that subsequent temperature regression can resolve sample spans of 0.02℃ / minute. If two consecutive valid windows are separated by only one invalid window, they are still considered continuous and included in the same candidate stationary time period record. The windows slide in 0.5-second increments with 75% overlap, allowing the start and end boundaries of stationary segments to be determined at a granularity of 0.5 seconds instead of 2 seconds, thus reducing the boundary positioning error to one-quarter of the window length.

[0030] Environmentally stable periods are obtained by performing temperature synchronization verification based on candidate stable periods and a temperature distribution array. Within the time interval corresponding to the candidate stable period, all temperature scanning points in that interval are extracted from the temperature distribution array. Linear regression of temperature versus time is performed on six measuring points, yielding a temperature change slope for each. The regression uses time as the independent variable and the temperature readings in the temperature distribution array as the dependent variable. This regression is executed in batches during the verification phase using a field-programmable gate array shared with phase demodulation, without a separate processor for the temperature channel. The regression channels for the six measuring points are executed in parallel without waiting for each other, and the total verification time does not increase linearly with the number of measuring points. Synchronization refers to verifying whether phase stability and temperature saturation are simultaneously established within the same interval. Measuring points with an absolute slope value lower than 0.02℃ / minute are considered to have reached temperature saturation within this interval. This threshold is the temperature change rate corresponding to twice the nominal resolution of 0.01℃ within a 1-minute window. When the slopes of all six measuring points simultaneously meet the condition, this candidate stable time period passes verification and is determined to be an environmentally stable time period, with the start and end timestamps of the interval recorded. If the slope of any measuring point exceeds the threshold, the verification process proceeds to the next candidate stable time period for further evaluation, and no environmentally stable time period is generated for this period. This situation typically occurs in the interval where the equipment's self-heating has not yet truly saturated, but the phase has temporarily leveled off due to brief fluctuations, requiring slope determination for identification. The first few candidate stable time periods immediately after the equipment is powered on are mostly eliminated one by one due to slope exceeding the limit. Usually, time periods that can pass verification begin to appear within 40 to 90 minutes after power-on, and thereafter the frequency of generating environmentally stable time periods gradually stabilizes.

[0031] The reference phase value is obtained by statistically analyzing the average phase value of the measurement points with the largest deviations during stable environmental periods. The phase reading of each measurement point during a stable period is the arithmetic mean of all sampling points in that period, yielding a representative value for that point. Six measurement points yield six representative values. The calculation of the reference phase value first removes the measurement point with the largest deviation: using the median of the six representative values ​​as a reference, the median is determined by the arithmetic mean of the third and fourth values ​​after sorting the six representative values ​​from smallest to largest. The absolute difference between the representative value of each measurement point and this median is calculated. The measurement point with the largest absolute difference is marked as the removal target. This measurement point typically corresponds to a location with significant stress concentration in the sensor head installation or a noticeable local micro-bend in the optical fiber. Its reading shows a systematic deviation relative to the other measurement points, and the direction of the deviation usually remains consistent across multiple power-on cycles. The arithmetic mean of the representative values ​​of the remaining five measurement points is then used as the reference phase value. This is calculated for each stable environmental period, with one reference phase value for each period. The exclusion criteria are determined independently for each time period. A measurement point that behaves abnormally in one time period may be judged as normal in another time period and become a member of the mean calculation. If the difference between the largest and second largest absolute differences within the same time period is less than 0.01 radians, this threshold is taken from the mean uncertainty of the noise background of the phase demodulation channel under the sample size of this time period. In this case, the measurement point with the largest deviation and the second largest deviation cannot be distinguished. The representative values ​​of the six measurement points are used together to participate in the arithmetic mean to obtain the reference phase value. The reference phase value, along with the representative values ​​of the six measurement points in this time period, the start and end times, and the exclusion criteria (if any), are archived together for the final step of verifying the deviation between measurement points by directly retrieving the representative values ​​of each measurement point and the exclusion criteria.

[0032] The reference phase value is determined by verifying the deviation between measurement points. First, the range between measurement points is calculated. Of the six representative values ​​recorded in the archive of all reference phase values, those marked as excluded in each time period are removed. The difference between the maximum and minimum values ​​of the remaining representative values ​​is then processed according to the range they fall into, with three cases handled based on the two boundary values ​​of the three criteria taken from the sensor head's factory inspection record. If the range does not exceed 0.03 radians (taken from the factory phase consistency qualification criterion), the representative values ​​of each measurement point are considered to be consistent, and the arithmetic mean of all reference phase values ​​is calculated to obtain the reference phase value. If the range exceeds 0.03 radians but does not exceed 0.06 radians (twice the criterion), and if the range of representative values ​​within the same time period still does not exceed 0.03 radians, meaning the excess originates from between time periods rather than between measurement points, it is determined to be a slow drift rather than a sudden change. In this case, the average of the last three consecutive reference phase values ​​in the time sequence is taken to determine the reference phase value. If there are fewer than three values, the reference phase value is determined after a new time period. When the range exceeds 0.06 radians, the reference phase value remains undetermined in this round of verification. The verification waits for a new stable environmental period to be generated and incorporated into the sample set. In the next round, only the last three consecutive reference phase values ​​in chronological order are used to recalculate the range, ensuring that the early, unstable periods are no longer retained in the sample set, preventing the range from falling back. The same three-level criteria are used for further judgment. If the range still does not fall into the first two levels after 10 rounds, the sensor is deemed to have a measurement point abnormality, an alarm is output, and the current round of compensation process is terminated. Once the reference phase value is determined, it remains fixed within the same power-on cycle. If the difference between the re-determined reference phase value and the retained value in the next power-on cycle does not exceed 0.03 radians, the retained value is used; updates are only made when the difference exceeds this value.

[0033] Step S102: Based on the phase waveform and the reference phase value, separate the heating and cooling paths to determine the phase offset section. Form the temperature drift rate curve by mapping the phase offset section and the temperature distribution array rate ratio. Use the temperature drift rate curve to perform lag time descending decoupling to construct the temperature drift curve.

[0034] In some embodiments, determining the phase offset segment based on the separation of the heating and cooling paths using the phase waveform and the reference phase value includes: performing a time-by-time comparison between the phase waveform and the reference phase value to generate a phase deviation record; marking the temperature rise and fall stages respectively based on the phase deviation record to obtain heating and cooling segment records; performing a phase comparison between two stages with similar rates at the same temperature point using the heating and cooling segment records to obtain a path offset record; and performing continuous deviation accumulation and aggregation in the same direction on the path offset record to determine the phase offset segment.

[0035] Phase deviation records are generated by comparing the phase waveform with the reference phase value at each time step. The phase waveform reading at each time step is subtracted from the reference phase value to obtain the phase deviation value at that time. This comparison covers all sampling times during the entire operating period after the equipment is powered on, without being limited to a single thermal cycle or distinguishing between heating and cooling stages. The same set of subtraction operations is performed indiscriminately at each time step. The reference phase value must be determined after self-heating saturation. The phase deviation at each sampling time step before that is recalculated by retrieving the stored phase waveform after the reference is determined. The recalculated result is written to the same record in the same format as the real-time result. Subsequent subtractions at each time step are completed in a pipelined manner within the field-programmable gate array (FPGA) synchronously with phase demodulation, without occupying an additional independent calculation cycle. The sign of the phase deviation is retained; a positive deviation indicates that the current phase waveform reading is higher than the reference phase value, and a negative deviation indicates the opposite. A zero value indicates that the phase at that time step has returned to the reference level. Each of the six measuring points independently completes the comparison. The deviation values ​​of the six measuring points at the same time are stored side-by-side in the same record line, arranged chronologically by timestamp. Each timestamp corresponds one-to-one with the original sampling time of the phase waveform. The comparison process itself does not perform interpolation or resampling; it directly reuses the sampling time reference established in S101. Each line of the phase deviation record also carries the temperature readings of the six measuring points at that time, directly taken from the same line of the temperature distribution array at the same time. These readings are used by the subsequent temperature rise / fall marking stages for each measuring point. The comparison itself only performs the subtraction operation between the phase and the reference phase value. The phase deviation records are stored sequentially in hourly split files. When the local capacity reaches its limit, the earliest file is transferred to external media instead of being discarded, allowing multiple subsequent steps to reuse the same underlying data.

[0036] Based on phase deviation recordings, temperature rise and fall phases are separately marked to obtain temperature rise and fall segment records. Temperature readings in the phase deviation record are compared at 6-second intervals, with the difference between adjacent nodes compared sequentially. Nodes with positive differences are marked as temperature rises, negative differences as temperature falls, and zero differences retain the previous node's mark. The 6-second node interval ensures that a typical temperature change of 0.5℃ / minute produces a 0.05℃ reading difference between adjacent nodes, reaching five times the 0.01℃ resolution of the temperature channel, preventing it from being overwhelmed by quantization noise. The remaining record lines between two nodes retain the node's mark, which is written back to the original record line as a single character. Marking and segmentation are performed independently for each measurement point. Within the same measurement point, consecutive nodes in the same direction are merged into a segment, forming one line of the temperature rise and fall segment record. The segment boundary is taken as the two adjacent nodes where the mark changes, and the boundary node is assigned to the new segment. A heating segment and its immediately following cooling segment constitute a thermal cycle. The start and end times of this cycle are the start and end times of the heating and cooling segments, respectively. To ensure that the same number points to the same process at each measuring point, the thermal cycle is not divided point-by-point. Instead, it is determined by taking the arithmetic mean of the temperature readings at six measuring points and marking the nodes. All six measuring points share the same set of thermal cycle numbers, which are incremented sequentially from 1. Upon restarting, the counting continues immediately from the last reading before the interruption. This number is then assigned to the corresponding segment at each measuring point: the segment's start and end timestamps intersect with the start and end times of the thermal cycle defined by the average temperature; the segment with the largest percentage of overlap is the corresponding thermal cycle. The temperature rise and fall segment records are written one by one. Each record corresponds to a segment of a measuring point and includes six items: measuring point number, thermal cycle number, start and end timestamps, temperature rise and fall direction indicator, temperature readings at the start and end of the segment, and phase deviation value. This allows subsequent steps to look up the start and end timestamps based on the number and return to the phase deviation record to retrieve the rows covered by the segment.

[0037] Path offset records are obtained by comparing the phase of two stages with similar rates at the same temperature point through segmented heating and cooling records. Each segmented heating and cooling record is scanned, and the phase deviation record is retrieved according to its start and end timestamps. The temperature readings already written back for each line of that segment are taken and rounded to a 0.1℃ grid; the rounded value is the temperature point. Time points with the same temperature point are identified in both the heating and cooling segments, and these two points are paired as candidate point pairs. Pairing is performed pairwise between each heating and cooling segment, not limited to adjacent heating and cooling cycles. Candidate point pairs are then filtered according to the temperature change rate of their respective heating and cooling segments. The rate is taken as the absolute value of the average rate of change of temperature over time within the segment. Only point pairs with a difference in heating and cooling rates not exceeding 20% ​​of the larger one are retained. This percentage is derived from the established criterion of consistent heating and cooling rates during factory inspection. Point pairs with excessively large rate differences are not comparable in terms of the thermal inertia states of the two stages and are not compared. For each retained point pair, the path offset is calculated point by point using the following formula: Δφ_offset,m(T)=φ_up,m(T)-φ_down,m(T), where m is the measurement point number, T is the temperature point value in degrees Celsius, φ_up,m(T) and φ_down,m(T) are the phase deviation values ​​of the temperature point during the heating and cooling stages of the m-th measurement point, respectively, in radians, taken from the phase deviation record, and Δφ_offset,m(T) is the path offset in radians, a positive value indicating that the heating path is higher than the cooling path. Each path offset record includes the measurement point number, the thermal cycle number to which the heating and cooling belong, the temperature point value, the heating phase deviation, the cooling phase deviation, and the path offset amount, and is arranged in two levels: measurement point and temperature point. The two phase deviations are used for the next step when calculating the rate proportion. The results of each temperature point are recorded separately to verify the degree of dispersion. If the range of each record exceeds half of the mean, the record for that point is returned to the rate screening and re-paired according to the stricter rate difference until it falls back before being included in the path offset record.

[0038] The path offset records are cumulatively aggregated in the same direction to determine the phase offset segments. The path offset records are first grouped by measurement point number. If multiple thermal cycle records exist for the same temperature point within a group, the arithmetic mean of their path offsets is taken and merged into one record for aggregation. This merging is only used for segment division in this step; the path offset record itself still retains all previous results. After merging, the records are arranged from low to high temperature point values. The sign of the path offset of adjacent records is checked point by point. Records with the same and consecutive signs are grouped into the same accumulation interval, and the position where the sign reverses is used as the interval boundary. The path offsets in each accumulation interval are summed one by one to obtain the total cumulative offset of the interval. Intervals with an absolute value of the total cumulative offset exceeding 0.02 radians are retained. This threshold is twice the uncertainty of the 0.01 radian phase mean described in S101. Intervals that do not exceed the threshold are considered noise fluctuations, and the temperature point range covered by them is merged into the side with the larger absolute value of the total cumulative offset between two adjacent temperature segments. If neither side exceeds the threshold, the range is temporarily not included in any segment. The phase shift segment consists of the retained cumulative intervals. Each segment is assigned a segment number from low to high according to the lower limit of the temperature range it covers. This number, along with the corresponding measurement point number, the temperature range covered, and the total cumulative shift, constitutes four items. The number of phase shift segments varies with the equipment's operating time and the temperature range covered by thermal cycling. The wider the coverage and the more temperature cycles experienced, the more finely the phase shift segments are divided. Early-established segments may be further subdivided into finer sub-segments as subsequent data is added. Once a segment is determined, it serves as a fixed basis for temperature zoning, allowing subsequent steps to establish a mapping relationship between the phase shift segments and the temperature distribution array.

[0039] The temperature drift rate curve is formed by mapping the phase offset segment to the temperature distribution array. The temperature drift rate curve is constructed separately for each measurement point, with one curve for each of the six measurement points. For each phase offset segment under each measurement point, all original temperature readings falling within its temperature range are first located in the temperature distribution array. Then, the phase-temperature change rate ratio of that segment is calculated using the following formula: r_j,m=Δφ_j,m / ΔT_j,m, where j is the phase offset segment number, m is the measurement point number, Δφ_j,m is the phase deviation change within that segment at the m-th measurement point, in radians, taken from the arithmetic mean difference of the phase deviations of the initial and final temperature points of that segment in the path offset record, ΔT_j,m is the corresponding temperature change, in degrees Celsius, taken from the difference between the values ​​of the two temperature points, and r_j,m is the phase change caused by a unit temperature rise in that segment, in radians per degree Celsius, calculated independently for each segment and each measurement point. The rate percentages are arranged sequentially according to the temperature range corresponding to each segment, forming a curve with temperature on the horizontal axis and rate percentage on the vertical axis. Each data point corresponds to a phase shift segment for that measurement point, and the horizontal axis is the midpoint temperature value of the segment's coverage area. If there is a blank area between two adjacent phase shift segments where no retained segment has yet appeared, the temperature drift rate curve fills the blank area with linear interpolation between adjacent points. The interpolation points are marked as calculated values ​​and distinguished from the measured points. The horizontal axis range of the temperature drift rate curve expands synchronously with the temperature coverage range of the phase shift segment; temperature intervals not yet experienced remain blank and are not extrapolated. The curve data points are arranged sequentially according to the temperature point values. In addition to the temperature coordinates and rate percentage, each point also records the sampling time range corresponding to all original temperature readings of that segment in the temperature distribution array, which is used by subsequent steps to extract the analysis window and extract the response lag time.

[0040] In some embodiments, the step of using the temperature drift rate curve to perform lag time descending order decoupling to construct the temperature drift curve includes: extracting the response lag time point by point using the temperature drift rate curve to obtain lag time records; determining the processing order based on the lag time records arranged in descending order of values; performing priority response compensation processing point by point according to the processing order and the lag time records to obtain a point-by-point correction curve; and performing time alignment splicing of each measurement point on the point-by-point correction curve to construct the temperature drift curve.

[0041] The response lag time is extracted point by point using the temperature drift rate curve to obtain the lag time record. For each temperature drift rate curve, data points marked as estimated values ​​are first removed. Then, among the remaining points, those with an absolute value of rate proportion not lower than the median of the measured points of this curve are selected. In sections with too low a proportion, the phase hardly moves with the temperature, and the peak time is indistinguishable. The sampling time range carried by the selected data points is returned to the temperature distribution array, and the time period with a temperature change rate exceeding 0.5℃ / minute is selected as the analysis window. The phase change rate is obtained by differentially analyzing the phase waveform point by point, and the temperature change rate is obtained by differentially analyzing the temperature distribution array point by point. The peak time of the phase change rate at the measurement point is taken, and the peak time of the temperature change rate within the same window is subtracted from the peak time of the phase change rate. The difference is the response lag time of this rapid change event. A positive value means that the phase lags behind the temperature. A negative value or a value exceeding the window length is judged as a false peak detection. The peak time is located by the maximum value point of the change rate sequence. To avoid misjudgment by single-point noise, the average change rate of the 5 points before and after it must still be the largest within the window to be recognized. If multiple conditions are met, the largest value is taken. Lag duration is recorded in seconds, and each event is calculated independently without advance averaging; the same temperature drift rate curve can correspond to multiple analysis windows. For example... Figure 2 As shown, the graph is divided into three columns: the top column is the rate of change domain, with thin lines representing the temperature change rate curve, vertical dashed lines indicating its peak time, and six thick lines representing the phase change rate curves at each measuring point; the middle and bottom columns are the phase domain, showing the afterimage and waveform before and after time shift at the first measuring point, respectively, as well as the result after fine-tuning. All three columns are arranged from top to bottom according to the processing order 2. Lag duration records are grouped and stored according to the measuring point number. The arithmetic mean of multiple response lag durations at the same measuring point is taken as the representative lag duration 1 for that measuring point. The representative value is recorded along with the number of events. If the number of events is less than 3, an insufficient sample mark is marked in the lag duration record.

[0042] The processing order is determined by sorting the lag duration records in descending order of value. The input for sorting only takes the representative lag duration column from the lag duration records: The representative value of each measurement point is read out one by one from measurement point number 1 to 6, forming a pair to be sorted. There are 6 pairs for 6 measurement points. Sorting is completed in a gate array register, with a total of 15 pairwise comparisons. Sorting uses a round-by-round selection of the maximum value: The representative values ​​are compared among the pairs yet to be retrieved, and the pair with the largest value is placed in the current empty position. Then, it is removed from the set to be sorted. This process is repeated until the set is empty. The resulting sequence is processing order 2, with the longest lag duration first and the shortest last. Taking six measurement points with lag times of 12.3 seconds, 9.8 seconds, 7.4 seconds, 5.1 seconds, 3.6 seconds, and 2.2 seconds as an example, the processing order after sorting is measurement points 1 to 6. Two groups with exactly the same representative value are placed in ascending order of measurement point number. If measurement points 3 and 4 both have a value of 7.4 seconds, then measurement point 3 remains first, ensuring a unique ranking. Measurement points marked with insufficient samples in the lag time record are still included in the sorting process, and their representative values ​​are not adjusted due to insufficient samples. The processing order is based on the fact that the longer the lag, the more significant the time misalignment of the phase waveform relative to the temperature change. Processing this measurement point earlier provides a time-aligned reference for processing subsequent measurement points, avoiding the situation where the reference itself still carries uncorrected lag errors due to a reversed processing order. The processing order record includes two items: the measurement point number and its corresponding ranking. Once determined, it remains fixed throughout the entire process of constructing the temperature drift curve and is passed to the next step of point-by-point compensation processing as the basis for the fixed order of traversing the 6 measurement points.

[0043] For example, the step of performing priority response compensation processing point by point according to the processing order and the lag duration record to obtain a point-by-point correction curve includes: determining the lag duration value of the current target measurement point based on the processing order and the lag duration record; performing phase reverse time shift processing based on the lag duration value to form a time-shifted waveform; performing residual deviation calculation on the time-shifted waveform and the reference phase value to obtain a connection correction amount; and performing error fine-tuning processing on the time-shifted waveform according to the connection correction amount to obtain a point-by-point correction curve.

[0044] The lag duration value of the current target measurement point is determined based on the processing order and lag duration records. The processing order is determined by sequentially retrieving the corresponding measurement point number from the first position, as the current target measurement point. After processing each measurement point, the processing order pointer advances to the next position until all six measurement points are processed and the pointer reaches the last position. The pointer advancement process records the list of currently completed measurement point numbers. Once the current target measurement point is determined, its representative lag duration is found in the lag duration record by measurement point number and used as the lag duration value for the current target measurement point. The search uses exact matching, without approximate matching or cross-measurement interpolation. The lag duration record is stored in groups by measurement point; the search locates the representative value column for that group, regardless of other fields such as the number of events. If the measurement point in the lag duration record is marked with an insufficient sample indicator, the search result still returns the representative value. However, if the measurement point fails the subsequent fine-tuning criteria, it will be preferentially reverted to the lag duration verification stage, rather than directly adopting the result of this round. The lag duration value of the current target measurement point, along with its number, is passed to the next time-shift processing stage. These two parameters are transmitted as a pair to ensure that the time-shift operation is accurately applied to the correct measurement point data and avoids misusing the lag duration values ​​of other measurement points. The correction results of already processed measurement points serve as reference benchmarks for subsequent measurement points in the time-shift and calculation stages. Measurement points processed later in the sequence can always refer to the correction results already obtained by earlier, longer-lag measurement points, forming a point-by-point recursive processing relationship. The loop executes for a total of 6 rounds, with each round corresponding to only one measurement point.

[0045] The phase-shifted waveform is generated by performing a phase-reverse time-shifting process based on the lag duration value. The phase waveform of the current target measurement point is shifted backward by 3 units along the negative time axis, corresponding to the lag duration value. That is, the value at time t after the shift is the value at the time corresponding to the sum of t before the shift and the lag duration. The shift direction is opposite to the lag direction, and the shift amount is numerically equal to the lag duration value itself. After the shift, the phase waveform, which originally lagged behind the temperature change due to response lag, is realigned with the temperature change on the time axis. The alignment effect is directly reflected in the time difference between the peak value of the shifted waveform and the peak value of the temperature of the same event approaching zero. The shift operation is performed on a discrete sampling sequence. If the lag duration value is not an integer multiple of the sampling period, the shift amount is rounded down by an integer number of sampling periods, with the rounding direction consistently downwards. Taking a measurement point with a lag of 9.87654 seconds as an example, this duration is equivalent to 98765.4 sampling periods at 10kHz sampling. After rounding down, the shift amount is 98765 sampling points, leaving 0.00004 seconds, which is less than one sampling period. The time error caused by rounding does not exceed one sampling period, and the error is recorded along with the shift amount without additional compensation. The end segment of the shifted waveform lacks corresponding data because it exceeds the original recording range. The missing end segment is filled by extending the value of the last available sampling point after the shift, and the filling length is the shift amount itself. The waveform after the time shift retains the original timestamp sequence unchanged; only the phase value shifts as a whole with the measurement point position. The timestamps still correspond one-to-one with the sampling time of the temperature distribution array, allowing subsequent steps to directly call them by time without realigning. The shift amount is retained along with the waveform after the time shift. During verification, it is only necessary to compare whether the peak time difference between the two waveforms before and after the time shift within the same event window has approached zero.

[0046] The residual deviation is calculated between the time-shifted waveform and the reference phase value to obtain the connection correction amount. The time-shifted waveform is subtracted from the reference phase value at each time step to obtain the phase deviation sequence remaining after the shift. The connection correction amount is calculated according to the following formula: δ_m=mean[φ_shift,m(t)-φ_base], where m is the measurement point number, t is the sampling time with an accuracy of 0.1 milliseconds, φ_shift,m(t) is the phase value of the time-shifted waveform at time t at the m-th measurement point, φ_base is the reference phase value, and both are in radians. mean[·] indicates that the arithmetic mean is taken in the stationary segment. δ_m is the connection correction amount at the m-th measurement point, in radians. The reference phase value is taken from the mean of the remaining measurement points after removing the measurement point with the largest deviation. The representative value of a single measurement point has an inherent deviation from it. This deviation, along with the rounding and extended residual, remains in the residual deviation sequence and must be calculated and deducted separately. The arithmetic mean of the residual deviation sequence within the stationary segment is the transition correction. The stationary segment is redefined on the waveform after time shift at each measuring point according to the environmental stationary period criterion identified in S101. Because the translation amounts of each measuring point are unequal, their start and end points are staggered accordingly. The sign of the transition correction is retained, and its value reflects the residual systematic difference between the waveform after time shift and the reference value. The transition correction is calculated point by point according to the processing order: the first point with the longest lag is referenced by the reference phase value; for each subsequent measuring point, the reference value is changed to the arithmetic mean of the reference phase value and the mean of the point-by-point correction curves of all the calibrated measuring points within the stationary segment of the current target measuring point. φ_base in the above formula is replaced by this updated reference value, and the update direction of this reference value is as shown in Figure 5. Figure 2 As shown. Because the steady segments of each measuring point do not overlap, the mean value of the curve of a completed measuring point within the steady segment of another does not necessarily have to be equal to the reference phase value, so that the reference value can be truly updated; the one with the longest lag is placed first, so as not to transmit the error in an uncorrected state.

[0047] The time-shifted waveform is fine-tuned using the coupling correction amount to obtain a point-by-point correction curve. Subtracting the same coupling correction amount 4 from each sampling point of the time-shifted waveform yields the point-by-point correction curve 6 for that measurement point, calculated as follows: φ_corr,m(t) = φ_shift,m(t) - δ_m, where φ_corr,m(t) is the phase value of the m-th measurement point at time t after fine-tuning, in radians. The subtraction applies the same value to the entire waveform, without adjusting the coupling correction amount based on time or temperature. The entire waveform uses the same constant and is not segmented. After fine-tuning, the difference between the peak moment of the phase change rate and the peak moment of the temperature change rate within the rapid change event window used to extract the lag duration of the point-by-point calibration curve should approach zero, serving as a direct criterion for whether the time shift is effective. Another criterion for the effectiveness of the fine-tuning is that the difference between the mean of the curve within the stable segment of this measurement point and the reference value should approach zero. Measurement points where the time difference still exceeds one comparison node interval need to be recalculated by reverting to the lag duration value verification stage. The point-by-point calibration curve retains the same timestamp sequence and sampling precision as the time-shifted waveform; only the overall numerical value shifts in the magnitude of the calibration amount. The waveform's shape, peak position, and trend remain unchanged due to the fine-tuning. After each of the six measurement points completes this stage in the processing order, each obtains an independent point-by-point calibration curve. Time dimension integration between measurement points has not yet been performed. The point-by-point calibration curve is a temporally continuous and complete sequence within each measurement point, sharing the same timestamp with the time-shifted waveform, with only an overall numerical shift. If a certain measuring point needs to recalculate the connection correction, it only needs to run the subtraction once again; however, since the reference value is gradually incorporated according to the processing order, all measuring points processed after this measuring point must be recalculated together, while the measuring points before it are not affected.

[0048] The temperature drift curve is constructed by time-aligning and stitching the point-by-point calibration curves at each measurement point. Since the point-by-point calibration curves 6 at each measurement point share the same original timestamp sequence, alignment along the time alignment line 7 does not require additional interpolation or resampling steps; it only requires directly matching the values ​​at the corresponding positions according to the timestamps. At the storage level, the alignment operation is equivalent to stitching six equal-length numerical sequences column-by-column. The stitching method involves taking the values ​​of the point-by-point calibration curves at each of the six measurement points at that moment, storing them side-by-side in the same time slice according to the measurement point number, and connecting the slices in the order of their timestamps to form a complete multi-measurement point time series. The slice structure is consistent with the phase waveform recording format of S101, facilitating the reuse of the same reading logic in subsequent steps. The temperature drift curve 8 represents the complete time series after stitching, covering the entire operating time since the equipment was powered on. Each time slice is assigned a continuous slice number starting from 1, containing the phase values ​​of 6 measurement points at that moment after hysteresis correction, as well as the temperature values ​​of 6 measurement points taken from the same time slice of the temperature distribution array. This gives the temperature drift curve both phase and temperature dimensions, allowing subsequent steps to directly calculate the phase slope against temperature based on adjacent data points. All phase values ​​are sourced from the point-by-point correction curve 6, without any original uncorrected phase readings. If a measurement point lacks an original sample value at a specific moment due to a channel fault during stitching, the corresponding measurement point position in that time slice is filled by linear interpolation of the point-by-point correction curve values ​​from adjacent moments. The interpolation points and the data points filled by the aforementioned time-shift extension are marked with source identifiers on the temperature drift curve to distinguish them from values ​​directly from the original samples. Both are excluded when extracting high-slope sections in subsequent steps. Subsequent steps extract high-slope sections from the temperature drift curve and calculate the temperature coefficient without modifying the curve itself.

[0049] Step S103: Generate candidate intervals for high-slope continuous sections of the temperature drift curve, calculate the extreme temperature range based on the candidate intervals and the reference phase value to obtain the initial temperature coefficient set, and perform cross-measuring point consistency verification and correction on the initial temperature coefficient set to output the temperature coefficient matrix.

[0050] Specifically, candidate intervals for generating coefficients are retained for continuous high-slope sections of the temperature drift curve. Data points are first extracted from the temperature drift curve according to the 6-second comparison node set in S102, ensuring that the temperature difference generated between adjacent points by a 0.5℃ / minute temperature change reaches 5 times the temperature channel resolution. Each group consists of 3 adjacent data points, and the local slope of the phase versus temperature is calculated for each group using the following formula: s_i,m=Δφ_i,m / ΔT_i,m, where i is the group number, m is the measurement point number, Δφ_i,m and ΔT_i,m are the phase difference and temperature difference between the first and last points of the group at the m-th measurement point, respectively, in radians and degrees Celsius, both taken from the same time slice of the temperature drift curve. s_i,m is the local slope of that group, in radians per degree Celsius. The calculation is performed by sliding between groups, with an overlap of 2 data points between groups and a step size of 1 data point. Data points with an absolute slope exceeding 0.008 radians per degree Celsius are marked as high-slope points. The threshold is the lower quartile of the phase-temperature slope distribution in the historical calibration data of this sensor model. Points below this threshold have slopes primarily determined by noise and are not included in interval formation. Marked points are checked for continuity within the time period covered by the same temperature rise / fall segment, according to their chronological order on the temperature drift curve. Points with an interval of no more than two unmarked points are considered continuous and merged into the same segment; points with an interval exceeding two or crossing segment boundaries are disconnected, ensuring monotonic temperature changes within the same segment and preventing the coverage area from reverting along the temperature curve. Candidate intervals for coefficients consist of continuous high-slope segments. Each interval is assigned an interval number from low to high according to the lower limit of the covered temperature range. This number, along with the corresponding measurement point number, the covered temperature range, and the start and end slice numbers on the temperature drift curve, constitutes four items for subsequent temperature zone division and point selection. If the temperature range covered by a candidate interval is narrower than 5°C, the sample size is insufficient, and they are only merged when the temperature intervals adjacent to each other are no more than 2°C apart.

[0051] In some embodiments, the step of obtaining an initial set of temperature coefficients by weighted calculation of extreme temperature regions based on the candidate coefficient interval and the reference phase value includes: dividing the extreme temperature regions and normal temperature regions at both ends of the temperature distribution based on the candidate coefficient interval; performing error calculation on the extreme temperature regions and normal temperature regions based on the reference phase value to obtain partition error records; performing differentiated hierarchical weighting on the partition error records to obtain weight configuration; and performing weighted fitting on the candidate coefficient interval according to the weight configuration to obtain an initial set of temperature coefficients.

[0052] Based on the candidate coefficient intervals, extreme temperature zones and normal temperature zones are divided at both ends of the temperature distribution. All candidate coefficient intervals under the measurement point are arranged according to the temperature range they cover. The difference between the lower limit of the lowest interval and the upper limit of the highest interval is taken as the total temperature span. 15% of this span is taken at both the lowest and highest points as the extreme temperature zone, and the middle 70% is designated as the normal temperature zone. The division ratio is taken from the predetermined ratio of temperature coefficient zoning calibration during the factory inspection of this sensor model. The division is based on the total temperature span covered by the candidate coefficient intervals, not the theoretical operating temperature range of the equipment. The extreme temperature zone is further divided into two sub-regions: a low-temperature extreme temperature zone and a high-temperature extreme temperature zone. These two sub-regions are not adjacent to each other and are separated by the normal temperature zone, and are recorded independently. Taking a measuring point with a total temperature range of -40℃ to 80℃ (a total of 120℃) as an example, 18℃ is taken at each end. The extreme low temperature zone is -40℃ to -22℃, the extreme high temperature zone is 62℃ to 80℃, and the remaining -22℃ to 62℃ is the normal temperature zone, which covers the temperature range most frequently encountered during the daily operation of the equipment. After the division, each interval in the candidate coefficient intervals is assigned to either the extreme temperature zone or the normal temperature zone according to the temperature range it covers. Intervals that cross boundaries and cover both zones are classified according to the side with the larger coverage width. Intervals with exactly equal coverage widths are classified according to the side with the lower temperature. The classification results, along with the partition records, are stored together for weighted fitting and point selection by partition. The extreme temperature zone and the normal temperature zone each record the candidate coefficient intervals assigned to them, a list of the candidate coefficient intervals listed in pairs according to the measuring point number and the interval number, the temperature range covered, and the total width of the interval. These three items serve as the partition basis for the next step of error calculation. The boundary is recalculated round by round as the coverage range of the candidate coefficient intervals increases, and remains unchanged within the current round.

[0053] Error calculations are performed on extreme temperature zones and normal temperature zones based on the reference phase value to obtain the zone error record. Before calculation, the temperature during each stable environmental period is obtained. Only the reference phase value corresponding to the period when the temperature falls into the normal temperature zone is re-averaged and used as the reference phase value for this step. For both extreme temperature zones and normal temperature zones, according to the start and end slice numbers recorded in the candidate coefficient intervals they belong to, all data points extracted from the temperature drift curve within that range at 6-second comparison nodes are retrieved. The difference between the phase value of each data point and the reference phase value is calculated. This difference represents the degree of phase deviation of this temperature point relative to normal temperature, and the positive or negative sign is retained. The root mean square of the difference within each range is calculated for the three zones: the squares of the differences are taken point by point, summed, divided by the total number of data points in the zone, and then the square root is taken to ensure that the positive and negative differences do not cancel each other out. The resulting root mean square is the representative value of the error level of the zone. The three zones are calculated independently and their data points are not mixed. The zone error record is stored according to the zone type. Each record contains two items: the zone type identifier and the representative value of the error level. There are a total of three records for the three zones. The representative values ​​for error levels typically show a pattern where the values ​​at the low and high temperature ends are higher than those at room temperature. For example, the representative values ​​for the three zones at a certain measuring point are 0.052 radians, 0.047 radians, and 0.011 radians, respectively, with the values ​​at both ends being more than four times those at room temperature. This reflects that the further the sensor deviates from room temperature, the greater the phase drift relative to the room temperature reference. This pattern is consistent with the common phenomenon that the refractive index and birefringence of optical fiber materials change more rapidly as the temperature deviates from room temperature. If the representative values ​​of two extreme temperature zones differ by more than double, the corresponding two zone error records are further annotated with asymmetry at both ends, indicating that there may be structural asymmetry in the heat transfer path inside the sensor head.

[0054] Weighting is achieved through differentiated hierarchical weighting of the partition error records. The representative error levels of the three partitions in the partition error records are sorted from largest to smallest, based entirely on the existing representative values ​​in the records. The partition with the highest error level is assigned the highest weight, followed by the middle partition, and the lowest partition is assigned the lowest weight. Weights increase sequentially with the magnitude of the representative error level, rather than being directly proportional to the value. Temperature drift is more significant in temperature zones that deviate more from the baseline, and their impact on compensation results is more severe. Therefore, their weight in the fitting process is increased to ensure the fitting results primarily conform to this temperature zone and are not biased by the more numerous normal temperature zones. The weighting uses a three-level fixed ratio: the partition with the highest error has a weight of 0.5, the partition with the middle error has a weight of 0.3, and the partition with the lowest error has a weight of 0.2. The sum of the three weights is always 1. This ratio is derived from a proven and effective allocation scheme in previous temperature coefficient calibrations of this sensor model and is not a temporary determination for this calculation. Taking a measuring point with representative values ​​of 0.052 radians, 0.047 radians, and 0.011 radians for the low-temperature extreme temperature zone, high-temperature extreme temperature zone, and normal temperature zone, respectively, as an example, the three are ranked from largest to smallest as the low-temperature extreme temperature zone, high-temperature extreme temperature zone, and normal temperature zone, with corresponding weights of 0.5, 0.3, and 0.2 in the weighting configuration. If, in another round of calculation, the representative value of the high-temperature end rises to 0.061 radians and the low-temperature end falls to 0.038 radians, the two zones are swapped, and the weights are changed to 0.3 and 0.5 respectively, while the normal temperature zone remains at 0.2. It can be seen that the zone assignment depends on the error level ranking in that calculation, rather than the inherent attributes of the measuring point. The zone assignment is re-determined based on the error record of that zone during each subsequent calculation, while the weight values ​​of the three zones in the weighting configuration remain fixed.

[0055] Weighted fitting is performed on the candidate intervals of the coefficients according to their weights to obtain the initial value group of temperature coefficients. All data points taken from the temperature drift curve according to the start and end slice numbers recorded for the candidate intervals are used in the fitting process, each with its corresponding weighted value. The fitting process uses temperature as the independent variable and phase as the dependent variable, performing a weighted linear fitting independently for each measurement point. The resulting fitting coefficients are the estimated slope of the phase change with temperature at that measurement point within the current temperature range. Simultaneously, the fitting residuals for that measurement point are output. The residuals are the root mean square of the sum of the squares of the weighted residuals of all participating points, in radians, and are included in the initial value group of temperature coefficients along with the initial values ​​for cross-measurement verification to identify the source of deviation. If multiple candidate intervals exist for the same measurement point, the data points from all intervals are merged into one batch for this fitting process, regardless of the interval's origin. In the weighted fitting, the weight of each data point is calculated by dividing the value corresponding to its partition in the weight configuration by the total number of data points within that partition. All data points within the same partition at the same measurement point share the same weight. This ensures that the total contribution of each partition to the fitting is strictly equal to the proportion determined by the weight configuration, preventing the extreme temperature regions from being overwhelmed by the dominance of data points in the normal temperature region. The slope estimate obtained after fitting is the initial value of the temperature coefficient for that measurement point, denoted as k_m, where m is the measurement point number, ranging from 1 to 6, and the unit is radians per degree Celsius. Its physical meaning is the phase change caused by a one-degree Celsius increase in temperature at the m-th measurement point. The initial temperature coefficient value group summarizes the k_m and fitting residuals for each of the six measurement points according to their measurement point numbers, grouping them one by one for each measurement point and six in total. Measurement points with larger residuals require special review during cross-measurement verification.

[0056] The initial temperature coefficient values ​​are checked and corrected across measurement points to output the temperature coefficient matrix. The initial values ​​of the six measurement points are compared pairwise. The absolute value of the difference between any two initial values ​​divided by the absolute value of their arithmetic mean is the relative difference for that measurement point pair. Pairwise combinations of the six measurement points generate 15 sets of differences. Measurement point pairs with a relative difference exceeding 15% are marked as inconsistent. This threshold is taken from the upper bound of the normal dispersion range among temperature coefficient measurement points in previous calibrations of the same batch of sensor heads. The marking results are recorded individually for each measurement point pair and are not summarized or statistically analyzed. If a measuring point is marked as abnormal by 3 or more of the other 5 measuring points (i.e., more than half), it indicates that the root cause of the inconsistency lies within the measuring point itself, not in the points being compared. Furthermore, if the fitting residual recorded in the initial temperature coefficient value group for that measuring point is more than twice the median of the residuals of the 6 measuring points, then the corresponding initial value for that measuring point is determined to have a deviation. The arithmetic mean of the initial values ​​of the remaining measuring points that are not determined to have a deviation is taken to replace the original initial value of that measuring point, and the original value before replacement is also retained for archiving. If the residual does not exceed this multiple, it indicates that the fitting itself is close, but the initial value deviation has another source; in this case, it is only marked as pending investigation without replacement. For measuring points that are not determined to have a deviation, the initial values ​​in their initial temperature coefficient value group are directly used without replacement or adjustment. After correction, the final temperature coefficient values ​​of the six measuring points, along with their corresponding hysteresis values, alignment corrections, and fitting residuals, form a row. This results in a five-column matrix consisting of the measuring point number, temperature coefficient, hysteresis value, alignment correction, and fitting residual. Each row corresponds to one measuring point, and each column corresponds to a type of parameter. The temperature coefficient matrix is ​​not recalculated within the same power-on cycle. If a measuring point requires maintenance and the sensor head assembly is replaced, only the row corresponding to that measuring point is recalculated; the entire matrix is ​​not rebuilt.

[0057] Step S104: Based on the phase offset segment, identify the increasing trend of hysteresis width in multiple thermal cycles to obtain the temperature drift hysteresis curve. Use the temperature drift hysteresis curve and the temperature coefficient matrix to reverse calibrate the hysteresis width to generate error compensation levels. Based on the error compensation levels, perform weighted verification of the compensation values ​​of adjacent levels to output a graded compensation strategy.

[0058] In some embodiments, the step of identifying the growth trend of hysteresis width across multiple thermal cycles based on the phase offset segment to obtain the temperature drift hysteresis curve includes: determining phase values ​​on both sides by performing phase extraction at the same temperature point according to the heating and cooling stages excluding the initial heating; forming a hysteresis width record by performing signed difference calculation at each temperature point based on the phase values ​​on both sides; obtaining a hysteresis width sequence record by sorting the hysteresis width record according to the chronological order of thermal cycles; and obtaining the temperature drift hysteresis curve by performing growth trend calculation on the hysteresis width sequence record.

[0059] Based on the phase shift section, phase extraction is performed at the same temperature point to determine the phase values ​​on both sides during the heating and cooling stages, except for the initial heating and cooling. Phase extraction in this step is only performed within the temperature range covered by the phase shift section; temperature points outside this range are not included. All thermal cycles numbered sequentially in the heating and cooling segment records are skipped because the numbers accumulate continuously from the start of power-on and continue counting after restarts. The first thermal cycle in each power-on cycle is not always numbered 1. Therefore, skipping is not limited to those numbered 1; rather, it skips all thermal cycles whose start time is earlier than the time when the reference phase value of that cycle is determined. This is because these types of thermal cycles have not yet undergone a complete saturation process, and their phase readings are relatively unstable. For each thermal cycle involved in the extraction, during its heating phase, temperature points overlapping with the phase shift segment are identified. The temperature values ​​of each time slice of the temperature drift curve are normalized using the same 0.1℃ grid. The slice with the normalized value equal to that temperature point is selected. The difference between the phase value of this measurement point after hysteresis correction and the reference phase value is the phase value on one side of the heating path. During the cooling phase of the same thermal cycle, the same temperature point is identified in the same way, and the corresponding difference is taken as the phase value on the other side of the cooling path. Phase deviation records without hysteresis correction are not used to avoid introducing a copy of apparent hysteresis in the same direction on both sides of the heating and cooling, which could be confused with hysteresis caused by stress relaxation. Point pairs are selected based on the larger of the heating and cooling rates in the path shift records, which should not differ by more than 20%, but both sides must belong to the same thermal cycle. Phase values ​​on both sides are generated in pairs for each measurement point and each temperature point. Each pair contains five items: measurement point number, thermal cycle number, temperature point value, and phase values ​​on both sides. Temperature points lacking data on either side will not generate phase values ​​on both sides. Temperature points whose values ​​are exactly equal to the upper and lower limits of the phase offset segment coverage area are considered to fall within that range. If the boundary values ​​of two adjacent segments are the same, they will be assigned to the side with the lower temperature.

[0060] Hysteresis width records are generated by performing signed difference calculations at each temperature point based on the phase values ​​on both sides. For each pair of phase values ​​on both sides, the difference calculation is performed point by point, retaining the sign and not taking the absolute value, and is calculated by the following formula: ΔH_m,n(T)=φ_up,m,n(T)-φ_down,m,n(T), where m is the measurement point number, n is the thermal cycle number, φ_up,m,n(T) and φ_down,m,n(T) are the phase deviation values ​​of the m-th measurement point on the heating and cooling paths of the nth thermal cycle, respectively, in radians, which are directly obtained from the phase values ​​on both sides. ΔH_m,n(T) is the signed hysteresis width of the temperature point, in radians, and a positive value indicates that the phase of the heating path is higher than that of the cooling path. Taking the third measuring point at the 35.0℃ temperature point in the 5th thermal cycle as an example, the phase values ​​on both sides are 0.412 radians on the heating path side and 0.385 radians on the cooling path side. Substituting these values ​​into the above formula, the hysteresis width at this point is 0.027 radians. Since both sides belong to the same thermal cycle and are at the same temperature point, they must fall within the same phase offset segment, and the calculation does not require further segmentation. This formula is the same as the S102 path offset calculation formula, except that in this formula, both sides must belong to the same thermal cycle and exclude self-heating unsaturated thermal cycles. Δφ_offset,m(T) allows cross-cycle pairing, and its cross-cycle averaging is completed separately in the aggregation stage. Each hysteresis width record contains four items: measuring point number, thermal cycle number, temperature point value, and ΔH_m,n(T), and is arranged in three levels according to the first three items. The magnitude of ΔH_m,n(T) reflects the degree of separation between the two heating and cooling paths at that temperature point. A value close to zero indicates that the two paths essentially overlap, while a larger value indicates a more pronounced separation. ΔH_m,n(T) at the same measuring point typically reaches its maximum value in the middle of the temperature span and approaches zero at both ends, with its absolute value generally not exceeding 0.1 radians. The hysteresis widths obtained at the same temperature point in different thermal cycles at the same measuring point are recorded independently. The number of hysteresis width records is determined by the number of thermal cycles involved in the extraction and the number of temperature points covered by the phase shift segment.

[0061] For example, obtaining the hysteresis width sequence record by sorting the hysteresis width records according to the order of thermal cycle occurrence includes: extracting the occurrence time corresponding to each thermal cycle from the hysteresis width records one by one to obtain a cycle time set; arranging the hysteresis width records in ascending order of value according to the cycle time set to form an initial sorting record; performing abnormal fallback identification based on the initial sorting record to generate an abnormal retention record; and confirming the sorting result of the abnormal retention record to obtain the hysteresis width sequence record.

[0062] The occurrence time of each thermal cycle is extracted from the hysteresis width record to obtain the cycle time set. The extraction proceeds sequentially according to the storage order of the hysteresis width records: the thermal cycle number carried by the current entry is read, and the segment with the direction identifier of heating and the same thermal cycle number is searched in the heating and cooling segment records using this number as the index. The start timestamp of the segment is taken as the occurrence time of the current thermal cycle. The timestamp is directly used and not recalculated. The accuracy is consistent with the heating and cooling segment records, down to 0.1 milliseconds. During the extraction process, a list of extracted numbers is maintained: each time a thermal cycle number is read, it is compared with the record. If it is already in the list, the search is skipped to the next entry. If it is not in the list, the above search is performed, and it is written into the cycle time set along with the obtained occurrence time, and the list is added at the same time. The list grows as the extraction progresses, and its length is the number of thermal cycles currently in the set. In hysteresis width records, the same thermal cycle number often corresponds to multiple records. The number of records corresponds to the number of temperature points covered by the thermal cycle. After the above comparison, only one occurrence time is extracted for each thermal cycle. Therefore, the number of items in the cycle time set is equal to the total number of thermal cycles participating in this round of identification, rather than the number of hysteresis width records. For example, for a measurement point covering 20 temperature points and undergoing 5 thermal cycles, there are approximately 100 hysteresis width records, while the cycle time set only has 5 items. Each item in the cycle time set contains two items: the thermal cycle number and the corresponding occurrence time. After being established, they are arranged in chronological order of occurrence time. The arrangement result is the chronological order of the thermal cycles. This order is usually consistent with the size order of the thermal cycle numbers. In rare cases where they are inconsistent, the occurrence time takes precedence.

[0063] The hysteresis width records are arranged in ascending order of value according to the cycle time set to form an initial sorting record. In this step, the hysteresis width records are first assigned to their respective thermal cycles according to the thermal cycle numbers listed in the cycle time set: entries in the hysteresis width record whose thermal cycle number is the same as a certain item in the cycle time set are assigned to that item. Under the same thermal cycle name, there are usually dozens of records, corresponding to the various temperature points it covers. Next, a representative value for the hysteresis width is taken for each thermal cycle. This representative value is the arithmetic mean of the absolute values ​​of all hysteresis width records within that thermal cycle. This is to prevent hysteresis widths with opposite signs at different temperature points from canceling each other out. For example, if the hysteresis width of a thermal cycle is -0.032 radians at low temperature and 0.028 radians at high temperature, directly taking the arithmetic mean yields -0.002 radians, almost zero. Taking the absolute value and averaging it yields 0.030 radians, which better reflects the actual hysteresis degree of that thermal cycle. The representative value is rounded to four decimal places, consistent with the dimensions and precision of the hysteresis width records, and corresponds one-to-one with the thermal cycle number in the cycle time set. The representative values ​​of the hysteresis width for all thermal cycles are rearranged in ascending order, and the result is the initial sorted record. Whether the order of the representative values ​​matches the chronological order of the occurrence times in the cycle time set is to be checked in the next step. Each initial sorting record contains three items: thermal cycle number, hysteresis width representative value, and sorted rank. In cases of tied rank and identical representative values, the thermal cycle number is used as the criterion for determining the tied rank. The initial sorting record and the cycle time set together serve as the input for the next step. The ranks start from 1 consecutively, with the smallest representative value ranking 1 and the largest ranking being the total number of thermal cycles.

[0064] Anomaly hysteresis identification is performed based on the initial sorted records to generate anomaly retention records. The rank order of the initial sorted records is compared with the cycle time set according to the chronological order determined by the occurrence time. Under normal circumstances, the representative value of the hysteresis width should gradually increase or remain stable as the thermal cycle occurs. If the representative value of a certain thermal cycle is significantly lower than the thermal cycle immediately preceding it, constituting a numerical hysteresis, and the hysteresis amplitude exceeds twice the standard deviation of the sequence, this cycle is marked as an anomaly hysteresis. The standard deviation is taken as the standard deviation of the sequence formed by the difference between two adjacent representative values ​​of all thermal cycles currently participating in the sorting, not the standard deviation of the representative value itself. The representative value increases monotonically with the thermal cycle, and its standard deviation is mainly contributed by the growth trend, with a value much larger than the amplitude of a single hysteresis. Based on this judgment, the anomaly hysteresis will be undetectable; it is recalculated every time the number of thermal cycles increases during successive identification. The hysteresis amplitude is taken as the absolute value of the difference between the representative value of the thermal cycle and the representative value of the thermal cycle that occurred earlier. Identification is performed sequentially from the earliest to the latest occurrence time, covering all thermal cycles that have participated in the sorting in one round. For thermal cycles marked as exhibiting abnormal decline, their corresponding initial sorting records are extracted separately and recorded along with the cycle's hysteresis width, occurrence time, and decline amplitude to form an anomaly retention record. The decline amplitudes in the anomaly retention record are arranged from largest to smallest for easy comparison of the deviation levels of different thermal cycles. For unmarked thermal cycles, their initial sorting records are retained as is, and their original rankings are not changed due to the existence of anomaly retention records. After the anomaly retention record is established, it, along with the initial sorting record, serves as input for the sorting result confirmation process. The number of entries in this record is dynamically determined based on the detection results and may be zero.

[0065] The sorting results of the retained abnormal records are confirmed to obtain the hysteresis width sequence. The sorting result confirmation is performed based on the initial sorting records and the cycle time set: all thermal cycles in the initial sorting records are ranked according to their representative values, and then reordered according to their respective occurrence times in the cycle time set, so that the final ranking is strictly consistent with the occurrence time sequence, and there are no more entries with contradictory ranking order and time order; for each entry in the retained abnormal records, the corresponding thermal cycle is marked with an abnormal fall after sorting. This mark is passed on to the next record with the hysteresis width sequence. The representative value of the marked entry is only retained as a data point in the subsequent growth trend calculation and does not participate in the fitting, so that the abnormalities detected by sorting by representative value size will not skew the growth trend. Taking the representative values ​​of 0.030 radians for the 7th thermal cycle, 0.021 radians for the 8th, and 0.034 radians for the 9th as examples, the 8th cycle, after being identified as having an abnormal drop, is included in the anomaly retention record. Its ranking remains between the 7th and 9th cycles according to the time of occurrence, and its representative value of 0.021 radians is retained as is. This point is only excluded in subsequent fitting to prevent the fitting slope from being lowered by this drop. The sorting adjustment only changes the order in which the thermal cycles appear in the final record; the representative values ​​themselves remain unchanged. The original hysteresis width representative values ​​and drop amplitudes in the anomaly retention record are retained; only their ranking changes. The complete sorting result after adjustment is the hysteresis width chronological record, each entry containing four items: thermal cycle number, time of occurrence, hysteresis width representative value, and final ranking. These are stored in ascending order of final ranking, representing the hysteresis width evolution order of all thermal cycles corrected chronologically.

[0066] The temperature drift hysteresis curve is obtained by performing growth trend calculation on the hysteresis width chronological records. The hysteresis width chronological records are extracted in the order of their final ranking, with the occurrence time corresponding to the ranking as the horizontal axis and the representative value of the hysteresis width as the vertical axis, and the points are connected to form a preliminary curve. Since the ranking of the records is uniformly arranged according to the occurrence time, the connection will not turn back along the horizontal axis. The preliminary curve only provides an overview of the overall evolution trend and does not participate in subsequent calculations. It is further divided into two dimensions: measurement point and temperature point. The signed hysteresis width of the same measurement point and the same temperature point in different thermal cycles is taken from ΔH_m,n(T) in the hysteresis width record. The hysteresis width chronological records only contain the representative value of the absolute value combined across measurement points and temperature points, and do not contain the value. The order of their arrangement is determined by the final ranking of the thermal cycle in the hysteresis width chronological records. Based on this, a unique evolution sequence for each measurement point and temperature point is formed, and each measurement point and each temperature point independently forms a sub-curve. The temperature drift hysteresis curve is composed of sub-curves for each measuring point and each temperature point. Each sub-curve records the measuring point number and temperature value. The horizontal axis represents the time of thermal cycle occurrence, and the vertical axis represents the signed hysteresis width of that measuring point at that temperature point. Different sub-curves share the same horizontal axis time reference. Each sub-curve performs linear fitting with the occurrence time as the independent variable and the signed hysteresis width as the dependent variable. The resulting slope is the hysteresis width growth rate g_m(T) of that measuring point at that temperature point, in radians per hour. Data points marked as abnormal declines are not included in the fitting, and their growth rates are stored along with the sub-curves in the temperature drift hysteresis curve. The number of data points on a sub-curve is equal to the number of thermal cycles corresponding to that temperature point in the hysteresis width record. If a temperature point appears only in a single thermal cycle, its sub-curve contains only one data point and does not constitute a curve segment from which the trend can be determined; the growth rate is recorded as zero.

[0067] Error compensation levels are generated by reverse calibration of the hysteresis width using the temperature drift hysteresis curve and the temperature coefficient matrix. For each measurement point and each temperature point in the temperature drift hysteresis curve, the hysteresis width of the latest thermal cycle is taken from the sub-curve. This width is then added to the product of the sub-curve's growth rate and the average interval between thermal cycles, i.e., extrapolating the increment of one thermal cycle. This interval is the arithmetic mean of the differences between two adjacent occurrence times within the cycle time set. The result is the present value of the hysteresis width. The present value is extrapolated based on the growth rate rather than using the historical average, ensuring that the compensation is based on the portion of hysteresis that will continue to accumulate after this calibration. Both the value and the growth rate are read from the temperature drift hysteresis curve. The temperature coefficient matrix is ​​searched for the corresponding row according to the measurement point number. The temperature coefficient k_m recorded in that row is taken, and the equivalent temperature deviation is calculated using the following formula: ΔT_eq,m(T)=ΔH_m(T) / k_m, where ΔH_m(T) is the present value of the hysteresis width at that temperature point, in radians, k_m is the temperature coefficient at that measurement point, in radians per degree Celsius, and ΔT_eq,m(T) is the equivalent temperature deviation, in degrees Celsius. Its physical meaning is: if the hysteresis width is entirely attributed to inaccurate temperature readings, then that temperature point is equivalent to having a temperature deviation of ΔT_eq,m(T). This formula is derived from the inverse solution of the forward relationship of the temperature coefficient matrix Δφ_m=k_m·ΔT_m, where ΔT_m is the temperature change at the m-th measurement point, and Δφ_m is the phase change it causes, in degrees Celsius and radians respectively. The direction is opposite to that of forward compensation, hence the name reverse calibration. The equivalent temperature deviation is divided into three levels based on its absolute value: not exceeding 0.5℃ is considered mild, 0.5℃ to 1.5℃ is moderate, and exceeding 1.5℃ is severe. The two dividing values ​​are taken from the allowable additional temperature error limit for the accuracy class of this model and three times that limit. These three levels are the level identifiers for the error compensation settings. The error compensation setting is recorded by the measurement point number and temperature point value, along with the identifier, the current value of the hysteresis width, and the equivalent temperature deviation. These three items together constitute a complete error compensation setting record.

[0068] A graded compensation strategy is adopted based on the weighted verification of adjacent compensation values ​​for error compensation levels. Error compensation level records are arranged according to temperature point values, and the level labels of adjacent temperature points are checked for consistency. For adjacent temperature point pairs with inconsistent level labels, the equivalent temperature deviation is weighted and averaged using the sequence number of the two levels as the weight (e.g., 3 for severe, 2 for moderate, and 1 for mild). This weighted average is compared with the original equivalent temperature deviation of the higher level in the pair. The absolute value of the difference is divided by the absolute value of the latter to obtain the relative difference. If the relative difference does not exceed 15%, the compensation values ​​at the level boundary are considered to be mutually weighted without introducing significant error, and the compensation values ​​of the two points are uniformly adopted according to this weighted average. For adjacent point pairs exceeding 15%, their original levels and compensation values ​​remain unchanged. Weighted verification is performed independently for each adjacent point, covering all adjacent combinations in the error compensation level record. If a temperature point is used as the comparison object on both sides and is determined to be weighted in both comparisons, its final compensation value is the arithmetic mean of the two weighted averages. If it is weighted only once, that result is used; if it is not weighted in either comparison, the original value is retained. The compensation values ​​after verification are reorganized to form a graded compensation strategy. Each graded compensation strategy records the measurement point number, temperature point value, final compensation value, and its corresponding level, arranged according to the first two items. The compensation value is retained to four decimal places in degrees Celsius, and the level identifier follows the original archived result before verification. The entries of the graded compensation strategy correspond one-to-one with the temperature points, and their density directly determines the density statistics of the subsequent compensation parameter table.

[0069] Step S105: Based on the hierarchical compensation strategy, density distribution is set to construct a compensation parameter table. The response rate adaptability is verified through the compensation parameter table to determine the corrected response weight. Based on the compensation parameter table and the corrected response weight, the jump response from room temperature to extreme temperature is verified to obtain the compensated voltage measurement result.

[0070] Specifically, a compensation parameter table is constructed based on the density distribution setting of the hierarchical compensation strategy. The compensation parameter table is constructed independently for each measurement point: For each measurement point number in the hierarchical compensation strategy, the number of entries within each 1°C interval is counted to determine the distribution density, with interval boundaries defined as integer degrees Celsius. The spacing between parameter points is set according to density segments: intervals with a density greater than 3 entries per degree Celsius are considered dense intervals, with one parameter point set every 0.5°C; intervals with no more than 3 entries per degree Celsius are considered sparse intervals, with one parameter point set every 2°C; intervals without any hierarchical compensation strategy entries are considered blank intervals and no parameter points are set. For each parameter point, the arithmetic mean of all the compensation values ​​within a range centered on that point and with a width equal to the distance between parameter points in this interval is taken, and denoted as the hysteresis equivalent temperature deviation ΔT_h,m(T), in degrees Celsius. The mean of the equivalent temperature deviation is then calculated using the following formula: ΔT_comp,m(T)=(T-T_room)+ΔT_h,m(T), where T is the temperature value of the parameter point, T_room is the ambient temperature reference temperature, taken as the rated operating ambient temperature value of the model, and both are in degrees Celsius; the first term is the main term of the steady-state temperature drift of that point relative to ambient temperature, and the second term is the additional deviation caused by hysteresis accumulation. The voltage compensation value is then converted using the following formula: ΔU_table,m(T)=-ΔT_comp,m(T)·k_m / K, where k_m is the temperature coefficient of the measuring point, in radians per degree Celsius, taken from the temperature coefficient matrix; K is the electro-optic conversion coefficient of this type of all-fiber voltage transformer, in radians per volt, taken from the factory inspection record; the negative sign is because the compensation value must be opposite to the deviation. The compensation parameter table records five items for each parameter point: measuring point number, temperature value, dense or sparse indicator, voltage compensation value, and representative range. These are stored in two levels, with the first two items being the most frequent range, for subsequent direct table lookup based on temperature value.

[0071] The corrected response weight is determined by verifying the adaptability of the response rate through a compensation parameter table. Adjacent parameter points in the table are paired, and the difference between their voltage compensation values ​​and the temperature difference gives the local response rate of that pair, in volts per degree Celsius. The calculation covers all adjacent combinations. Pairs crossing dense and sparse intervals are identified by their recorded markings and calculated based on their actual temperature difference. The local response rate is compared with the measured inherent thermal response rate of the voltage transformer within that temperature range. The inherent thermal response rate is the inherent rate of change of the output voltage of the sensor model with temperature within this range, also in volts per degree Celsius, taken from the temperature-added error calibration data in the factory inspection record. Both are dimensionless; the ratio of their absolute values ​​yields the dimensionless number. The compensation value must be inversely proportional to the temperature drift, and its rate of change must be opposite in sign to the inherent thermal response rate; therefore, the absolute value must be taken first for comparison. The closer the ratio is to 1, the closer the compensation amount given in the table is to the actual voltage deviation generated by the equipment; the farther it deviates from 1, the less the value density in the table keeps up with the actual temperature response of the equipment. The corrected response weight is the reciprocal of this ratio, truncated to between 0.5 and 2: a ratio less than 1 indicates that the compensation amount is too small, and its reciprocal is greater than 1, which is used to strengthen subsequent transient calculations; a ratio greater than 1 indicates the opposite; for point pairs with ratios between 0.7 and 1.3, the corrected response weight falls between 0.77 and 1.43, close to the reference value of 1, and is marked as having good adaptability. The corrected response weight, along with the corresponding measurement point number and temperature range, is recorded and stored in two levels; when there are blank intervals in the compensation parameter table, the reference value of 1 is used at the corresponding gap, so that subsequent step settings and transient calculations still have definite values ​​available at that gap.

[0072] In some embodiments, the step of verifying the jump response from room temperature to extreme temperature based on the compensation parameter table and the corrected response weight to obtain the compensated voltage measurement result includes: setting the corrected response weight to a step from room temperature to extreme temperature to form a stable change curve; performing step-by-step waiting and transition interval segmentation on the stable change curve to output a jump response signal; performing dynamic compensation calculation in the unsteady-state interval based on the jump response signal and the corrected response weight to determine the transient compensation value; and performing superposition based on the compensation parameter table and the transient compensation value to obtain the compensated voltage measurement result.

[0073] A stable change curve is formed by setting the corrected response weights in stepwise increments from room temperature to the extreme temperature. Under conditions such as diurnal temperature variations, sudden cold snaps, and power outages causing sudden heating and shutdowns, the ambient temperature can fluctuate significantly within a short period. Due to thermal inertia, the sensor head's phase readings do not synchronize with the temperature during the transition phase. Therefore, it is necessary to verify the corrected response weights point-by-point using stepwise increments covering room temperature to the extreme temperature. Starting from the room temperature reference temperature T_room and ending at the equipment's specified high and low temperature limits, step points are set sequentially with a standard interval of 5℃. For corrected response weights falling outside the range of 0.77 to 1.43 (i.e., not marked as well-suited) and for parameter points representing high-intensity settings, the step point interval is increased to 2.5℃. Although the step is based on temperature, its density is determined by the corrected response weights interval by interval; hence, this is called setting the corrected response weights in stepwise increments. If a step point coincides with a parameter point in the compensation parameter table, the target compensation value is directly taken as the voltage compensation value of that parameter point. If they do not coincide, the value is obtained by linear interpolation between adjacent points. All step points are arranged in the order of rising from room temperature to high temperature, then falling back from high temperature to room temperature to low temperature, and finally rising back from low temperature to room temperature, forming a step sequence. Step points are numbered consecutively starting from 1 in this order. Each point in the step sequence contains four items: step point number, target temperature, target compensation value, and the correction response weight corresponding to the interval in which the point is located. For each step point, the theoretical waiting time required for stabilization is determined by looking up a table based on its correction response weight. The table values ​​are taken from the calibration data of the time required for thermal equilibrium under different weight intervals during factory inspection, and a maximum waiting time of three times this maximum waiting time is given as the upper limit. The waiting time, the maximum waiting time, and the four items recorded in the step sequence together constitute the stable change curve. The stable change curve records the step occurrence sequence, target temperature, and two durations point by point. The ambient temperature setting during execution is taken from the target temperature in the stable change curve.

[0074] The step-by-step waiting and transition interval segmentation output jump response signal is performed through the stable change curve. The waiting progresses point by point along the step sequence recorded on the stable change curve: at each step point, the ambient temperature setting is kept constant according to the waiting time recorded on the stable change curve for that point. The time range from the switching time to the full waiting time is the waiting interval. After the full waiting time, it moves to the next point. The switching command is issued in advance according to the curve sequence and is linked with the temperature control equipment. The voltage reading of the all-fiber voltage transformer is not directly measured through a separate channel, but is calculated from the phase waveform: the voltage reading at a certain measuring point t is U_m(t) = φ_m(t) / K, where φ_m(t) is the phase waveform reading at the measuring point at t, in radians, and K is the aforementioned electro-optic conversion coefficient, in radians per volt. Therefore, the voltage reading and the phase waveform share the same sampling time and the same clock source, without introducing additional channel differences. At the moment of each step transition and for a period thereafter, the voltage reading fluctuates nonlinearly due to sudden changes in ambient temperature. The acquired waveform is segmented according to the moment of the step, with each step corresponding to an independent output waveform segment, which is the jump response signal. The jump response signal covers the complete transition interval from the moment of the step until the waveform returns to stability. Whether it has reached stability uses the stability scanning criterion of S101, only dividing its phase standard deviation threshold by the electro-optic conversion coefficient K to convert it into a voltage threshold before applying it to the voltage reading; the criterion parameters are not defined separately. The length of the transition interval is determined independently for each step, and its upper limit is the longest waiting time recorded at that step point on the stable change curve. The jump response signal is archived independently for each step, with the sampled value recorded in volts, and the timestamp aligned with the moment of the step. The jump response signal is generated independently for each measurement point; each of the six measurement points calculates a voltage reading from its own phase waveform, all originating from the same set of phase sampling timing.

[0075] The transient compensation value is determined by performing dynamic compensation calculation in the unsteady-state interval based on the jump response signal and the corrected response weight. For each step, all sampling points of its jump response signal within the transition interval are taken; this interval is the unsteady-state interval. The transient deviation is obtained by subtracting the theoretical stable voltage value of the step from the reading at each point. The theoretical stable voltage value is calculated by the following formula: U_stable,m,p=U_room,m-ΔU_table,m(T_p), where m is the measurement point number, p is the step point number, U_room,m is the ambient temperature reference voltage reading at the measurement point, T_p is the temperature of the step point in degrees Celsius, and ΔU_table,m(T_p) is the voltage compensation value of the measurement point at T_p in the compensation parameter table. The units of the three voltage quantities are volts. The minus sign is used because the voltage compensation value already has a negative sign, so this value is the position that the reading should reach after stabilization. The ambient temperature reference voltage reading is taken from the calibration reading of the current transformer measured at T_room under the same measured voltage, and calibrated point by point at 6 measurement points. The transient deviation reaches its maximum at the instant of the step and converges monotonically as the heat of the sensor head redistributes. The convergence rate is determined by the thermal time constant of the sensor head itself, so it must be compensated point by point rather than taking the same value for the whole segment. The transient deviation is multiplied point by point by the correction response weight of the interval in which the step point is located and the sign is negative, i.e., ΔU_transient,m(t)=-w_m·e_m(t), where e_m(t) is the transient deviation at the m-th measurement point in volts, w_m is the correction response weight of the interval in dimensionless form, and the result is the transient compensation value, rounded to 4 decimal places in volts; the transient deviation is amplified when the weight is greater than 1, and reduced when it is less than 1. The transient compensation value corresponds one-to-one with the sampling point of the jump response signal and is stored in a three-level arrangement according to the measurement point number, step point, and sampling time. Taking a sampling point 0.5 seconds after a step as an example, its reading is 0.0120 volts lower than the theoretical stable voltage value. The weight of this interval is 1.25. Substituting this value, we get a transient compensation value of 0.0150 volts. As the transition interval progresses, the reading gradually approaches this value, and the transient compensation value approaches zero.

[0076] The compensated voltage measurement result is obtained by superimposing the compensation parameter table and transient compensation value. For each sampling moment, the original voltage reading is used to find the voltage compensation value in the compensation parameter table corresponding to its respective step point and the transient compensation value at the same moment. The step point of a given sampling moment is determined by the waiting interval of which step recorded on the steady-state curve its timestamp falls into, specifically the new step after the transition between two steps. Superposition involves taking the sum of these three values: the original voltage reading calculated from the phase waveform at that moment, the voltage compensation value in the compensation parameter table at that step point temperature, and the transient compensation value at that moment. The result is the compensated voltage measurement result for that measurement point at that moment, with all three values ​​and the result rounded to four decimal places in volts. The former offsets the voltage deviation caused by steady-state temperature drift at that temperature point, and the latter offsets the deviation caused by the reading not yet being accurate during the transition phase. Both are opposite to their respective deviations; their sum brings the reading back to its correct position. Within the steady-state range, the transient compensation value is set to zero. The voltage measurement result after compensation is obtained solely by superimposing the original reading with the voltage compensation value from the compensation parameter table, and then returns to the ambient temperature reference voltage reading. This means the compensated reading no longer changes with ambient temperature. The result sequence is reassembled according to the original sampling time order and generated independently for each measurement point. Each measurement point only takes its own compensation parameter table and transient compensation value. The result sequences from the six measurement points are merged into a single output at each time step: using the median of the six values ​​at the same time as a reference, the measurement point with the largest absolute difference from the median is removed, and the arithmetic mean of the remaining five measurement points is calculated. This result is the voltage measurement result after compensation for the transformer, and the results from each measurement point are stored together for retrospective analysis. The voltage measurement result after compensation records five items at each time step: sampling time, original voltage reading, voltage compensation value from the compensation parameter table, transient compensation value, and the compensated value. The source of compensation at that time can be traced back based on the latter three items.

[0077] To implement the above-described method embodiment, a temperature compensation measurement method for an all-fiber voltage transformer is provided to achieve the corresponding functions and technical effects. See also... Figure 3 , Figure 3 This diagram illustrates a structural block diagram of a temperature compensation measuring device 300 for an all-fiber voltage transformer according to an embodiment of this application. For ease of explanation, only the parts relevant to this embodiment are shown. The all-fiber voltage transformer temperature compensation measuring device 300 provided in this embodiment includes:

[0078] Phase acquisition module 301 is used to acquire phase waveforms and temperature distribution arrays at multiple measurement points, and to identify self-heating saturation and eliminate stable sections based on the phase waveforms and temperature distribution arrays to determine the reference phase value.

[0079] Path decoupling module 302 is used to separate the heating and cooling paths based on the phase waveform and the reference phase value to determine the phase offset segment, form a temperature drift rate curve by mapping the phase offset segment and the temperature distribution array rate ratio, and use the temperature drift rate curve to perform lag time descending order decoupling to construct the temperature drift curve.

[0080] The coefficient calibration module 303 is used to generate candidate intervals of coefficients by retaining the high-slope continuous section of the temperature drift curve, calculate the extreme temperature range based on the candidate intervals of coefficients and the reference phase value to obtain the initial value group of temperature coefficients, and perform cross-measuring point consistency verification and correction on the initial value group of temperature coefficients to output the temperature coefficient matrix.

[0081] The gear calibration module 304 is used to identify the increasing trend of hysteresis width of multiple thermal cycles based on the phase offset segment to obtain the temperature drift hysteresis curve, and to generate an error compensation gear by reverse calibration of the hysteresis width through the temperature drift hysteresis curve and the temperature coefficient matrix. Based on the error compensation gear, the adjacent gear compensation values ​​are weighted and verified to output a graded compensation strategy.

[0082] The compensation output module 305 is used to construct a compensation parameter table based on the density distribution setting of the hierarchical compensation strategy, determine the corrected response weight by verifying the response rate adaptability through the compensation parameter table, and obtain the compensated voltage measurement result by verifying the jump response from room temperature to extreme temperature based on the compensation parameter table and the corrected response weight.

[0083] The aforementioned all-fiber voltage transformer temperature compensation measurement device can implement the all-fiber voltage transformer temperature compensation measurement method described in the above method embodiments. The options in the above method embodiments are also applicable to this embodiment, and will not be detailed here. The remaining contents of this application embodiment can be referred to the contents of the above method embodiments, and will not be repeated in this embodiment.

[0084] The purpose of the above embodiments is to reproduce and derive the technical solution of the present invention by way of example, and to fully describe the technical solution, purpose and effect of the present invention. The purpose is to enable the public to have a more thorough and comprehensive understanding of the disclosure of the present invention, and not to limit the scope of protection of the present invention.

Claims

1. A method for measuring temperature compensation in an all-fiber voltage transformer, characterized in that, include: Collect phase waveforms and temperature distribution arrays from multiple measurement points, and use the phase waveforms and temperature distribution arrays to identify self-heating saturation, eliminate stable sections, and determine the reference phase value. Based on the phase waveform and the reference phase value, the heating and cooling paths are separated to determine the phase offset segment. The phase offset segment and the temperature distribution array are mapped to form a temperature drift rate curve. The temperature drift rate curve is used to perform hysteresis decoupling to construct the temperature drift curve. The high-slope continuous section of the temperature drift curve is retained to generate candidate intervals for coefficients. Based on the candidate intervals for coefficients and the reference phase value, the extreme temperature region is weighted and calculated to obtain the initial temperature coefficient value group. The initial temperature coefficient value group is then corrected by cross-measuring point consistency verification and output as a temperature coefficient matrix. Based on the phase offset segment, the temperature drift hysteresis curve is obtained by identifying the growth trend of the hysteresis width of multiple thermal cycles. The hysteresis width is then calibrated in reverse using the temperature drift hysteresis curve and the temperature coefficient matrix to generate error compensation levels. Based on the error compensation levels, the compensation values ​​of adjacent levels are weighted and verified to output a graded compensation strategy. Based on the graded compensation strategy, a compensation parameter table is constructed by setting the density distribution. The response rate adaptability is verified through the compensation parameter table to determine the corrected response weight. Based on the compensation parameter table and the corrected response weight, the jump response from room temperature to extreme temperature is verified to obtain the voltage measurement result after compensation.

2. The method according to claim 1, characterized in that, The step of determining the reference phase value by identifying the self-heating saturation exclusion of stable sections based on the phase waveform and the temperature distribution array includes: The phase waveform is subjected to time-by-time stability scanning to obtain candidate stable time periods; Based on the candidate stable time period and the temperature distribution array, a temperature synchronization verification is performed to obtain the environmental stable time period; The reference phase value is obtained by statistically analyzing the average phase value after removing the measurement point with the largest deviation during the stable environmental period. The reference phase value is determined by performing a deviation verification between measurement points.

3. The method according to claim 1, characterized in that, The step of determining the phase offset segment based on the separation of the heating and cooling paths according to the phase waveform and the reference phase value includes: A phase deviation record is generated by comparing the phase waveform with the reference phase value at each time step. Based on the phase deviation record, the temperature rise and fall stages are marked to obtain the temperature rise and fall segment record; The path offset record is obtained by performing a phase comparison between two stages with similar rates at the same temperature point through the temperature rise and fall segment record; The phase offset segment is determined by performing continuous deviation accumulation and aggregation on the path offset record in the same direction.

4. The method according to claim 1, characterized in that, The step of constructing the temperature drift curve by performing lag time descending decoupling using the temperature drift rate curve includes: The response lag time is extracted point by point using the temperature drift rate curve to obtain the lag time record; The processing order is determined by arranging the lag duration records in descending order of their values. Based on the processing order and the lag duration record, priority response compensation processing is performed point by point to obtain a point-by-point correction curve; The temperature drift curve is constructed by aligning and splicing the time of each measuring point on the point-by-point calibration curve.

5. The method according to claim 1, characterized in that, The process of obtaining the initial set of temperature coefficients by weighting and calculating the extreme temperature range based on the candidate coefficient interval and the reference phase value includes: Based on the candidate coefficient interval, the extreme temperature zone and the normal temperature zone at both ends of the temperature distribution are divided. Based on the reference phase value, error calculation is performed between the extreme temperature zone and the normal temperature zone to obtain the partition error record; The weight configuration is obtained by performing differentiated hierarchical weighting based on the partition error records; The candidate intervals of the coefficients are subjected to weighted fitting according to the weight configuration to obtain the initial value group of the temperature coefficients.

6. The method according to claim 1, characterized in that, The method of identifying the increasing trend of hysteresis width across multiple thermal cycles based on the phase shift segment to obtain the temperature drift hysteresis curve includes: Based on the phase offset section, phase extraction at the same temperature point is performed to determine the phase values ​​on both sides during the heating and cooling stages, excluding the initial heating stage. Based on the phase values ​​on both sides, a signed difference calculation is performed at each temperature point to form a hysteresis width record; The hysteresis width sequence records are obtained by sorting the hysteresis width records according to the order of thermal cycle occurrence. The temperature drift hysteresis curve is obtained by calculating the growth trend of the recorded hysteresis widths.

7. The method according to claim 1, characterized in that, The step of verifying the jump response from room temperature to extreme temperature based on the compensation parameter table and the corrected response weights to obtain the compensated voltage measurement results includes: The corrected response weights are set to a stable change curve by stepping from room temperature to the limit temperature. The step-by-step jump response signal is output by dividing the transition interval through the stable change curve; Based on the jump response signal and the corrected response weight, perform dynamic compensation calculation in the unsteady-state interval to determine the transient compensation value; The voltage measurement result after compensation is obtained by superimposing the compensation parameter table and the transient compensation value.

8. The method according to claim 4, characterized in that, The step-by-step correction curve is obtained by performing priority response compensation processing point by point according to the processing order and the lag duration record, including: The lag time value of the current target measurement point is determined based on the processing order and the lag time record; Based on the lag duration value, a phase-reverse time-shifting process is performed to form a time-shifted waveform; The residual deviation between the time-shifted waveform and the reference phase value is calculated to obtain the connection correction amount; The time-shifted waveform is fine-tuned according to the aforementioned connection correction amount to obtain a point-by-point correction curve.

9. The method according to claim 6, characterized in that, The process of obtaining the hysteresis width sequence record by sorting the hysteresis width record according to the chronological order of thermal cycling occurrence includes: The cycle time set is obtained by extracting the occurrence time corresponding to each thermal cycle from the hysteresis width record; The hysteresis width records are arranged in ascending order of value according to the cycle time set to form an initial sorted record; Based on the initial sorted records, perform abnormal fallback identification to generate abnormal retention records; The abnormal retained records are sorted to confirm the order of hysteresis width records.

10. A temperature compensation measuring device for an all-fiber voltage transformer, characterized in that, include: The phase acquisition module is used to acquire phase waveforms and temperature distribution arrays at multiple measurement points, and to identify self-heating saturation and eliminate stable sections based on the phase waveforms and temperature distribution arrays to determine the reference phase value. The path decoupling module is used to separate the heating and cooling paths based on the phase waveform and the reference phase value to determine the phase offset segment, form a temperature drift rate curve by mapping the phase offset segment and the temperature distribution array rate ratio, and use the temperature drift rate curve to perform lag time descending order decoupling to construct the temperature drift curve. The coefficient calibration module is used to generate candidate intervals for coefficients by retaining the high-slope continuous section of the temperature drift curve, calculate the extreme temperature range based on the candidate intervals and the reference phase value to obtain the initial temperature coefficient value group, and perform cross-measuring point consistency verification and correction on the initial temperature coefficient value group to output the temperature coefficient matrix. The gear calibration module is used to identify the increasing trend of hysteresis width in multiple thermal cycles based on the phase offset segment to obtain the temperature drift hysteresis curve. The hysteresis width is calibrated in reverse by the temperature drift hysteresis curve and the temperature coefficient matrix to generate the error compensation gear. The error compensation gear is used to weight and verify the compensation values ​​of adjacent gears and output a graded compensation strategy. The compensation output module is used to construct a compensation parameter table based on the density distribution setting of the hierarchical compensation strategy, determine the corrected response weight by verifying the response rate adaptability through the compensation parameter table, and obtain the compensated voltage measurement result by verifying the jump response from room temperature to extreme temperature based on the compensation parameter table and the corrected response weight.

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