Temperature compensation method for thermistor power sensors

Abstract

This invention discloses a temperature compensation method for a thermistor power sensor, relating to the field of sensor compensation technology. It solves the problem of how to quickly and accurately predict the steady-state power value of a thermistor power sensor before thermal equilibrium is established, and effectively overcomes technical problems such as thermal response hysteresis and dynamic errors caused by frequency, aging, and environmental changes. The method includes: acquiring the transient power sequence of the thermistor power sensor, extracting an amplitude feature sequence from it, and determining a rate feature sequence accordingly; weighting the rate feature sequence based on the current operating frequency and combining it with the amplitude feature sequence to obtain a composite feature vector; performing approximation matching calculations on the composite feature vector with multiple sets of standard frequency response features to determine the combination coefficients; synthesizing multiple standard extrapolation factors based on the combination coefficients to obtain a synthetic extrapolation factor suitable for the current operating condition, and combining it with the transient power sequence to determine the extrapolated steady-state power.

Description

Technical Field

[0001] This invention relates to the field of sensor compensation technology, and specifically to a temperature compensation method for a thermistor power sensor. Background Technology

[0002] In the field of microwave and millimeter-wave power metering, thermistor power sensors are core devices based on the DC substitution method. They infer the RF input power by measuring the change in DC bias power required to maintain a constant thermistor temperature, and are widely used in various precision testing and measurement scenarios. To address the effects of the sensor's own thermal inertia and ambient temperature fluctuations, existing technologies typically employ a temperature compensation strategy based on a frequency lookup table, which statically corrects the measurement results according to a preset calibration factor. However, this static compensation mechanism struggles to adapt to the dynamically changing thermal response characteristics of sensors under complex actual operating conditions. Consequently, in broadband applications where rapid measurement is crucial, it is often difficult to balance overall measurement accuracy and efficiency, leaving room for improvement. Summary of the Invention

[0003] To address the current technical challenges of rapidly and accurately predicting the steady-state power value of a thermistor power sensor before thermal equilibrium is established, and to effectively overcome thermal response hysteresis and dynamic errors caused by frequency, aging, and environmental changes, this invention aims to provide a temperature compensation method for thermistor power sensors. The specific technical solution adopted is as follows: In a first aspect, the present invention provides a temperature compensation method for a thermistor power sensor, comprising: acquiring a transient power sequence generated by the thermistor power sensor under input power excitation within a preset observation period; extracting an amplitude feature sequence from the transient power sequence and determining a rate feature sequence based on the amplitude feature sequence; wherein the rate feature sequence is used to characterize the rate of change of the thermal response waveform over time; weighting the rate feature sequence based on the current operating frequency and combining the weighted rate feature sequence with the amplitude feature sequence to obtain a composite feature vector; wherein the composite feature vector is used to comprehensively characterize the morphology and transient change characteristics of the thermal response waveform; performing approximation matching calculations on the composite feature vector and multiple sets of standard frequency response features to determine a combination coefficient; wherein the combination coefficient is used to characterize the matching weight between the current thermal response waveform and each standard frequency response waveform; synthesizing multiple preset standard extrapolation factors corresponding to each standard frequency point according to the combination coefficient to obtain a synthetic extrapolation factor applicable to the current operating condition, and determining the extrapolated steady-state power based on the synthetic extrapolation factor and the transient power sequence.

[0004] Secondly, the present invention provides a temperature compensation system for a thermistor power sensor, comprising: a data acquisition module for acquiring a transient power sequence generated by the thermistor power sensor under input power excitation within a preset observation period; a feature sequence construction module for extracting an amplitude feature sequence from the transient power sequence and determining a rate feature sequence based on the amplitude feature sequence; wherein the rate feature sequence is used to characterize the rate of change of the thermal response waveform over time; and a composite feature construction module for weighting the rate feature sequence based on the current operating frequency and combining the weighted rate feature sequence with the amplitude feature sequence. A composite feature vector is obtained; the composite feature vector is used to comprehensively characterize the morphology and transient change characteristics of the thermal response waveform; the modal approximation solution module is used to perform approximation matching calculations on the composite feature vector and multiple sets of standard frequency response characteristics to determine the combination coefficients; the combination coefficients are used to characterize the matching weight between the current thermal response waveform and each standard frequency response waveform; the steady-state reconstruction output module is used to synthesize multiple preset standard extrapolation factors corresponding to each standard frequency point according to the combination coefficients to obtain the synthetic extrapolation factor applicable to the current operating condition, and determine the extrapolated steady-state power according to the synthetic extrapolation factor and the transient power sequence.

[0005] Thirdly, the present invention provides an electronic device, comprising: a processor and a memory; wherein the memory is used to store one or more programs, the one or more programs including computer-executable instructions, wherein when the electronic device is running, the processor executes the computer-executable instructions stored in the memory to cause the electronic device to perform a temperature compensation method for a thermistor power sensor as described in the first aspect and any possible implementation thereof.

[0006] The present invention has the following beneficial effects: by acquiring short-time transient power sequences, extracting and constructing composite features that integrate amplitude and frequency weighted rate information, using these features to approximate and match with a standard feature library to dynamically determine the combination coefficients, and then synthesizing customized extrapolation factors based on these coefficients, and finally combining baseline, anchor power and ambient temperature compensation to quickly and accurately predict steady-state power values, effectively overcoming dynamic measurement errors caused by factors such as thermal inertia, frequency changes, device aging and environmental fluctuations, and realizing high-precision and rapid power measurement when thermal equilibrium has not been reached. Attached Figure Description

[0007] To more clearly illustrate the technical solutions and advantages in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0008] Figure 1 This is a schematic flowchart of a temperature compensation method for a thermistor power sensor provided in one embodiment of the present invention; Figure 2 This is a schematic diagram of the architecture of a temperature compensation system for a thermistor power sensor provided in one embodiment of the present invention. Detailed Implementation

[0009] To further illustrate the technical means and effects adopted by the present invention to achieve its intended purpose, the specific implementation methods, structures, features, and effects of the present invention will be described in detail below with reference to the accompanying drawings and preferred embodiments. In the following description, different "one embodiment" or "another embodiment" do not necessarily refer to the same embodiment. Furthermore, specific features, structures, or characteristics in one or more embodiments can be combined in any suitable form.

[0010] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0011] The following describes in detail, with reference to the accompanying drawings, a specific scheme for a temperature compensation method for a thermistor power sensor provided by the present invention.

[0012] For example, such as Figure 1 The diagram shown is a schematic flowchart of a temperature compensation method for a thermistor power sensor according to an embodiment of the present invention, including the following steps: S101. Obtain the transient power sequence generated by the thermistor power sensor under input power excitation within a preset observation period.

[0013] In this embodiment of the invention, the transient power sequence specifically refers to a set of power sample values ​​arranged in chronological order, acquired by the thermistor power sensor within a fixed time window much shorter than its thermal equilibrium time after the application of radio frequency input power. For example, this fixed time window can be set to 10 milliseconds. Its setting requires a trade-off between measurement speed and feature integrity: on the one hand, the window should be much shorter than the second-level time required for the sensor to reach thermal equilibrium to meet the need for rapid measurement; on the other hand, the window needs to be long enough to fully capture the rising edge waveform containing key morphological and rate-of-change information in the initial stage of the thermal response, typically covering the phase from the trigger point to the relatively gradual change in the response. Based on a typical sampling frequency of 10 kHz, 10 milliseconds correspond to 100 sampling points, which effectively meets the above requirements.

[0014] Optionally, the transient power sequence generated by the thermistor power sensor during a preset observation period under input power excitation can be obtained through the following steps: (1) Continuously collect the bridge output voltage of the thermistor power sensor.

[0015] The output voltage of the thermistor power sensor's bridge circuit can be obtained in real time by connecting a high-precision analog-to-digital converter (ADC) to the output port of the sensor's Wheatstone bridge. Specifically, the ADC synchronously samples and digitizes the differential voltage across the bridge at a fixed sampling frequency, obtaining a series of voltage sample values ​​arranged in chronological order.

[0016] (2) When the rate of change of the bridge output voltage exceeds the preset trigger threshold, the first preset number of sampling points before the corresponding time is extracted to form a background segment, and the second preset number of sampling points after the corresponding time is extracted to form a response segment.

[0017] In this step, the rate of change of adjacent voltage sample values ​​is calculated in real time (i.e., the voltage value of the previous sample point is subtracted from the voltage value of the subsequent sample point, and the difference is the voltage change between the two points; this voltage change is then divided by the time interval between the two samplings to obtain the rate of change of adjacent voltage sample values), and compared with a preset trigger threshold to accurately capture the start time of the application of radio frequency input power. Once the rate of change exceeds the threshold, that moment is determined as the trigger moment. The background segment consists of continuous voltage sample points with a length of a first preset number before the trigger moment, used to characterize the sensor's background state before the application of radio frequency power. The response segment consists of continuous voltage sample points with a length of a second preset number after the trigger moment, used to fully cover the sensor's dynamic thermal response within a preset observation period.

[0018] For example, the aforementioned preset trigger threshold is set based on the background noise statistical characteristics of the thermistor power sensor when there is no RF input power, to ensure that the real power input signal can be effectively distinguished from system noise. For example, a segment of background noise data can be collected in a no-signal state, the standard deviation of its voltage change rate can be calculated, and the preset trigger threshold can be set to 3 to 5 times that standard deviation.

[0019] Furthermore, the aforementioned first preset quantity can be set to 100, and the rule for setting this quantity is: this quantity should ensure that the extracted background segment has sufficient length to calculate a stable value that characterizes the sensor’s noise floor and average power value at the DC operating point when there is no RF power input (i.e., baseline power), while avoiding excessive length that would lead to unnecessary resource occupation of the circular buffer.

[0020] Furthermore, the aforementioned second preset quantity can be set to 200, and the rule for its value is: the length of the observation period corresponding to this quantity (e.g., 20 milliseconds) should be much shorter than the second-level time required for the sensor to reach thermal equilibrium, but it must be long enough to fully cover the rising edge of the thermal response waveform in the initial stage, which contains key morphological and rate of change information, so as to provide effective dynamic data for subsequent feature extraction.

[0021] (3) The background segment and the response segment are spliced ​​together to form the original voltage sequence, and the original voltage sequence is converted into a power sequence and then smoothed and filtered to obtain the transient power sequence.

[0022] Optionally, based on the sensor's calibration coefficients, each voltage value in the original voltage sequence is converted into a corresponding instantaneous power value, forming a preliminary power sequence. To further suppress high-frequency measurement noise, this power sequence is smoothed using a preset low-pass digital filter (such as a moving average filter or a Butterworth low-pass filter). The cutoff frequency of the smoothing filter must be higher than the sensor's primary thermal response frequency to preserve the true dynamic change trend.

[0023] Thus, this step yields a set of power data, filtered out of high-frequency noise, characterizing the sensor's dynamic thermal response within a short observation window, i.e., a transient power sequence, laying the data foundation for feature extraction and analysis in subsequent steps.

[0024] S102. Extract the amplitude feature sequence from the transient power sequence, and determine the rate feature sequence based on the amplitude feature sequence. The rate feature sequence is used to characterize the rate of change of the thermal response waveform over time.

[0025] It should be noted that the amplitude characteristic sequence is a set of normalized numerical sequences that eliminate the influence of absolute power values ​​and only reflect the relative morphological changes of the thermal response waveform. The rate characteristic sequence, on the other hand, is a set of numerical sequences obtained by differentiating the amplitude characteristic sequence and reflecting the instantaneous slope of the waveform.

[0026] This step aims to extract essential dynamic features related to sensor thermal inertia and frequency effects from the raw transient power data. Specifically, firstly, the baseline power characterizing the starting point of power change and the anchor power characterizing the state at the end of the observation period are determined from the background and response segments. These are then used to normalize the power values ​​in the response segment, obtaining an amplitude feature sequence that is only related to the waveform geometry. Subsequently, the amplitude feature sequence is differentially calculated to obtain its gradient, and the gradient value is converted into a time-dimensional value (in seconds) by dividing by the sampling time interval. -1 ), a rate feature sequence characterizing the instantaneous change rate of the normalized amplitude. It should be noted that the specific procedures for determining the baseline power and anchoring power, as well as the normalization and difference calculations in the aforementioned sub-steps, can be found in S201-S204 below, and will not be repeated here.

[0027] Thus, this step separates two key feature sequences from the original transient power sequence, representing the "shape" and "rate of change" of the response, respectively, providing data basis for constructing higher-order composite features.

[0028] S103. The rate feature sequence is weighted based on the current operating frequency, and the weighted rate feature sequence is combined with the amplitude feature sequence to obtain a composite feature vector. The composite feature vector is used to comprehensively characterize the morphology and transient change characteristics of the thermal response waveform.

[0029] It is understandable that the current operating frequency is the frequency of the radio frequency input power signal currently applied to the thermistor power sensor. Furthermore, the composite feature vector is a high-dimensional vector that concatenates amplitude shape information with frequency-weighted transient change information.

[0030] The purpose of this step is to construct a highly discriminative feature that simultaneously reflects the essential form of the thermal response and incorporates the influence of frequency physics. Specifically, since the sensor's thermal response rate to different frequencies is affected by factors such as the skin effect, a frequency-related weight value is first calculated based on the current operating frequency. This weight value is usually positively correlated with the frequency to amplify the importance of the rate characteristics at high frequencies. Then, each element in the rate feature sequence is multiplied by this weight value to achieve weighting. Finally, the weighted rate feature sequence is concatenated with the previously extracted amplitude feature sequence in terms of dimension, forming a composite feature vector that includes waveform "shape" information and frequency-modulated "rate of change" information. It should be noted that the specific procedures for calculating the frequency-related weight value and feature concatenation in the aforementioned sub-steps can be found in S301-S303 below, and will not be repeated here.

[0031] Thus, this step generates a composite feature vector that can more comprehensively and sensitively characterize the dynamic thermal response of the sensor at the current specific operating frequency, providing input for subsequent accurate matching with the standard feature library.

[0032] S104. Perform approximation matching calculations between the composite feature vector and multiple sets of standard frequency response features to determine the combination coefficients. The combination coefficients characterize the matching weights between the current thermal response waveform and each standard frequency response waveform.

[0033] Specifically, the multiple sets of standard frequency response features are based on a pre-stored standard response library. They are constructed using the same rules as those used to construct the current composite feature vector (same observation window, normalization method, differential processing, and frequency weighting rules), creating a set of feature vectors for multiple standard frequency points, either pre-constructed or constructed in real-time. The combination coefficients are a set of non-negative values, each corresponding to a standard frequency point. The sum of all coefficients is 1, and their magnitude reflects the similarity between the currently measured composite feature vector and the corresponding standard feature vector (i.e., the standard frequency response features).

[0034] This step aims to use mathematical methods to decompose the current thermal response waveform, which may be distorted due to frequency shift, device aging, or environmental interference, into a linear combination of multiple ideal standard frequency response waveforms. Specifically, firstly, the multiple sets of standard frequency response features are acquired or generated based on a pre-stored standard response library, and arranged to form a composite reference matrix. Then, using the current composite feature vector as the target and the composite reference matrix as the basis, a linear least squares problem with non-negativity constraints is solved to find an optimal set of combination coefficients such that the result obtained by linearly combining the basis features with these coefficients is closest to the current composite feature vector. It should be noted that the specific procedures for standard feature acquisition, reference matrix construction, and mathematical solution in the aforementioned sub-steps can be found in S401-S402 below, and will not be repeated here.

[0035] Thus, this step yields a set of quantified combination coefficients, which reveal the similarity between the current actual thermal response waveform and the ideal response waveform at various standard frequencies, providing a basis for dynamically synthesizing extrapolation factors.

[0036] S105. Based on the combination coefficient, synthesize multiple standard extrapolation factors corresponding to each standard frequency point according to the preset combination coefficient to obtain the synthesized extrapolation factor applicable to the current operating condition, and determine the extrapolated steady-state power based on the synthesized extrapolation factor and the transient power sequence.

[0037] Among them, the multiple standard extrapolation factors corresponding to each standard frequency point are preset vectors consisting of theoretical multiples required to extrapolate the transient power value at the end of the observation window to the steady-state power value in complete thermal equilibrium when measuring each standard frequency input under calibration conditions.

[0038] Furthermore, the synthetic extrapolation factor, calculated based on the combination coefficient and the standard extrapolation factor, is a dynamically calculated extrapolation multiple applicable to the current specific operating condition, based on the degree of matching between the current measured waveform and the standard waveform (i.e., the combination coefficient). This extrapolation factor is used to extrapolate the short-term observed transient power value to the steady-state value that should be reached when it reaches complete thermal equilibrium. The uncorrected steady-state power value is a preliminary result obtained by extrapolation calculation using only the synthetic extrapolation factor. The extrapolated steady-state power is the final high-precision power measurement result output after environmental temperature compensation.

[0039] This step aims to dynamically generate a customized extrapolation factor using the matched combination coefficients, and ultimately calculate a high-precision steady-state power prediction. The process for determining the synthetic extrapolation factor is as follows: (1) If the result of the approximation matching calculation meets the preset fitting quality conditions, the composite extrapolation factor is calculated by weighting the multiple preset standard extrapolation factors according to the combination coefficient.

[0040] For example, the preset fit quality condition can be set to the relative residual. The sum of the combined coefficients must be less than the relative residual threshold, and greater than the coefficient sum threshold. The aforementioned relative residual threshold can be set to 0.1, and its value is determined according to the system's allowed prediction error range to determine the effectiveness of the mathematical approximation. The coefficient sum threshold can be set to 0.001 to prevent the coefficient sum from being close to zero due to numerical issues in the algorithm, ensuring the numerical stability of the weighted composite calculation.

[0041] In this case, it is shown that the currently measured thermal response waveform can be well linearly represented by the standard waveform library. For example, the synthetic extrapolation factor is calculated using the following formula: in, This represents the synthetic extrapolation factor. This represents the combination coefficient corresponding to the k-th standard frequency response, which characterizes the matching weight between the current waveform and the standard waveform. This represents the total number of standard frequency response characteristics.

[0042] The above formula uses a weighted average calculation. The numerator is calculated using the combination coefficient. As weights, for all preset standard extrapolation factors A weighted sum is performed, and then divided by the sum of all weights (combination coefficients) (the denominator) to obtain a synthetic extrapolation factor that integrates information from multiple standard factors and is optimized and adjusted according to the current waveform matching weights. .

[0043] (2) If the result of the approximation matching calculation does not meet the preset fitting quality conditions, the corresponding factor is found from the preset multiple standard extrapolation factors according to the current working frequency and used as the synthetic extrapolation factor.

[0044] In this case, it indicates that the measured waveform is severely distorted and cannot match well with the standard library, so the system activates the rollback mechanism. Fit quality conditions typically involve judging the residuals of the approximation matching calculation. When this condition is not met, based on the current operating frequency, the corresponding standard extrapolation factor is directly obtained from the standard frequency points through linear interpolation as the synthetic extrapolation factor for this measurement, ensuring the reliability of basic functions.

[0045] Furthermore, the process for determining the extrapolated steady-state power is as follows: (3) Obtain the anchor power and baseline power determined based on the transient power sequence, and calculate the steady-state power value without environmental correction based on the anchor power, baseline power and synthetic extrapolation factor.

[0046] This step aims to extrapolate the transient power increment within the observation window to the theoretical total increment at thermal equilibrium using a synthetic extrapolation factor, thereby predicting the steady-state power. Optionally, the steady-state power value without environmental correction is calculated using the following formula: in, This represents the steady-state power value without environmental correction. This represents the anchored power, which is the power sample value of the transient power sequence at the end of the observation period. This represents the baseline power, which is the average power value of the background segment before the application of radio frequency power. This represents the synthetic extrapolation factor.

[0047] The above formula performs a linear extrapolation calculation. First, it calculates the net power increment within the observation window. Then multiply it by the synthetic extrapolation factor. This yields the predicted total heat balance increment. Finally, this total increment is compared with the baseline power. Adding them together yields the predicted steady-state power value, without environmental correction. .

[0048] (4) Obtain the current ambient base temperature, and compensate the uncorrected steady-state power value based on the ambient base temperature, the pre-stored reference temperature and the temperature sensitivity coefficient to obtain the extrapolated steady-state power.

[0049] Furthermore, to eliminate the influence of ambient temperature fluctuations on sensor thermal parameters (such as thermal conductivity), a second-order correction is applied to the predicted steady-state power to improve the final measurement accuracy. The extrapolated steady-state power is calculated using the following formula: in, This represents the extrapolated steady-state power, which is the final output measurement result. This represents the steady-state power value without environmental correction. The temperature sensitivity coefficient, as specified in the factory calibration, characterizes the rate of change of the sensor's power reading with ambient temperature. Its unit is typically % / °C or 1 / °C. Its absolute value reflects the magnitude of the effect of ambient temperature change on the sensor's power reading, while its sign directly reflects the direction of the effect. This coefficient is derived from... The data is fitted by measuring the sensor response to varying ambient temperatures in the vicinity. Therefore, if the actual environmental influence is an increase in temperature leading to a lower reading, the fitted data will be less accurate. >0, making the compensation factor If the value is greater than 1, the reading is corrected upwards; otherwise, it is corrected downwards. The ambient base temperature is measured in real time by the auxiliary temperature probe built into the sensor. The reference temperature, usually 25°C, is the ambient temperature reference when the sensor is calibrated at the factory.

[0050] The above formula performs linear temperature compensation. First, it calculates the difference between the current ambient temperature and the reference temperature. Then multiply by the temperature sensitivity coefficient η to obtain the relative change in power reading caused by temperature change. Add 1 to this change and then compare it with the uncorrected steady-state power value. Multiply, thus affecting Scaling compensation is performed to obtain a more accurate extrapolated steady-state power. .

[0051] The extrapolated steady-state power obtained in this step is the predicted RF input power value that the thermistor power sensor should indicate in a fully thermally balanced state after dynamic waveform correction and ambient temperature compensation. This value is used to replace the actual measured value after a long waiting period, thus achieving fast and high-precision power measurement.

[0052] Based on the above technical solution, this invention acquires short-time transient power sequences, extracts and constructs composite features that integrate amplitude and frequency weighted rate information, uses these features to perform approximation matching with a standard feature library to dynamically determine the combination coefficients, and then synthesizes customized extrapolation factors based on these coefficients. Finally, by combining baseline, anchor power, and ambient temperature compensation, the steady-state power value can be predicted quickly and accurately. This effectively overcomes dynamic measurement errors caused by factors such as thermal inertia, frequency changes, device aging, and environmental fluctuations, and achieves high-precision and rapid power measurement even when thermal equilibrium has not been reached.

[0053] For example, in another temperature compensation method for a thermistor power sensor provided in one embodiment of the present invention, the amplitude feature sequence is extracted from the transient power sequence, and the rate feature sequence is determined based on the amplitude feature sequence, specifically including the following steps: S201. Calculate the average power of the background segment in the transient power sequence as the baseline power.

[0054] Specifically, baseline power This represents the baseline power level when the sensor measurement bridge is in equilibrium before the application of RF input power, and is used to eliminate the effects of zero-point drift and background noise in subsequent calculations. This step determines the baseline power by calculating the arithmetic mean of all power samples in the background segment, as shown in the following formula: Where M represents the total number of sampling points contained in the background segment, i.e., the first preset number. This represents the power value at the i-th sampling point in the transient power sequence. The above calculation uses the arithmetic mean of the background power data. This involves taking M consecutive power samples within the background segment. Add them together, then divide by the total number of points M to obtain the average value, which is used as a stable and reliable background power reference value. .

[0055] S202. Calculate the power value of the sampling point at the end of the response segment in the transient power sequence, and use it as the anchor power.

[0056] Specifically, anchoring power This represents the instantaneous power amplitude reached by the sensor's thermal response at the end of the preset observation period, serving as the amplitude reference for the transient response captured within the current short-time observation window. This step determines the anchoring power by directly extracting the value of the last sampling point in the response segment of the transient power sequence; its expression is: in, This represents the power value at the (M+N)th sampling point in the transient power sequence. Here, M is the background segment length, and N is the response segment length (i.e., the second preset number). Therefore, M+N corresponds to the last point in the entire transient power sequence (background segment + response segment), that is, the end of the response segment. The operation represented by the above formula is direct data indexing. Based on the sequence structure, the power value of the specific sampling point corresponding to the end of the observation window in the transient power sequence is located and read, and then assigned... , which serves as a reference for the amplitude of the current transient response.

[0057] S203. Based on the transient power sequence, baseline power, and anchoring power, the response segment is normalized to obtain the amplitude characteristic sequence.

[0058] Furthermore, this step aims to eliminate the influence of the absolute amplitude of the input power on waveform shape analysis, converting the thermal response curves at different power levels into comparable dimensionless sequences that only reflect geometric morphology. First, the validity of the signal needs to be determined: the dynamic power range needs to be calculated. In addition, a first effective signal threshold is preset. Used to determine if a signal is weak. For example, Possible value: 1×10 −7 The value of W is determined by the following rules: This threshold is usually set to a value that is slightly higher than the noise level of the sensor system (e.g., 3 to 5 times the root mean square noise value), or determined according to the minimum measurable power requirement, so as to ensure that the subsequent complex compensation algorithm is executed only when the power change caused by the input power is significantly higher than the system's noise level fluctuation, thus avoiding invalid calculations for noise or false triggering signals.

[0059] Furthermore, if < If the signal is invalid, the process terminates. ≥ Then, the response segment is normalized. For each sampling point within the response segment... (where t = 1, 2, ..., N), calculate its normalized value. Thus forming an amplitude feature sequence After this processing, the generated sequence The numerical range of the waveform monotonically increases from near 0 at the start time to strictly equal to 1 at the end time, thus stripping away the absolute power magnitude and retaining only the shape and curvature of the waveform. It should be noted that, due to... After passing the first effective signal threshold The comparison judgment is used, so the value will not be zero in this formula.

[0060] S204. Perform differential calculation on the amplitude feature sequence, and determine the rate feature sequence based on the differential result and the sampling time interval.

[0061] Finally, information about the rate of thermal diffusion, reflecting the speed of change, is extracted from the normalized waveform morphology. This feature is sensitive to frequency changes (especially the skin effect). First, the amplitude feature sequence... First-order difference operations are performed to obtain the change between adjacent points. Then, in order to eliminate the influence of different sampling rates in the data acquisition system and to ensure that the rate characteristics have a uniform physical dimension (1 / second), the difference result must be divided by the system's sampling time interval. For the t-th point in the sequence (t≥2), its corresponding rate characteristic value is... Calculated using the following formula: in, The value at point t in the rate characteristic sequence represents the normalized rate of change of the thermal response near time t. This represents the value of the t-th point in the amplitude feature sequence. This represents the value at the (t-1)th point in the amplitude feature sequence. It represents the sampling time interval and is the reciprocal of the sampling frequency of the data acquisition system.

[0062] The above formula calculates the discrete difference and unifies the time dimension. The numerator calculates the difference between two adjacent normalized amplitude points, reflecting the local variation of the waveform at that point. This difference is then divided by the sampling time interval. This involves approximating the discrete difference as the derivative with respect to time, thereby obtaining the normalized rate of change in units of "seconds," forming a rate characteristic sequence. This sequence effectively characterizes the instantaneous rate of change of the thermal response waveform at different times.

[0063] It should be noted that the above formula applies to calculating the rate characteristic value from the second point onwards in the sequence. For the starting point of the rate characteristic sequence (i.e., t=1), since there is no preceding point (t=0) available for calculating the backward difference, a boundary processing method is required. This boundary processing method ensures that the obtained rate characteristic sequence... Compared with the original amplitude feature sequence They have the same length (denoted as N). Optionally, the forward difference method is used to process the boundary point, that is, the instantaneous rate of change at time t=1 is approximated by using the data of two points t=1 and t=2. The specific calculation process is common knowledge and will not be described here.

[0064] Based on the above technical solution, this embodiment of the invention obtains amplitude features that purely reflect the geometry of the thermal response by accurately calculating the baseline power and anchoring power and using them to normalize the transient response. Furthermore, by performing time-dimension-unified differential calculations on these amplitude features, the rate of change directly related to the physical process of thermal diffusion is extracted. This combined feature extraction method lays a solid foundation for subsequently constructing composite feature vectors that integrate morphological and dynamic information, effectively overcoming the limitations of single amplitude features being susceptible to noise interference and insensitive to changes in frequency, etc.

[0065] For example, in another temperature compensation method for a thermistor power sensor provided in one embodiment of the present invention, the rate feature sequence is weighted based on the current operating frequency, and the weighted rate feature sequence is combined with the amplitude feature sequence to obtain a composite feature vector, specifically including the following steps: S301. Calculate the frequency correlation weight value based on the current operating frequency. The frequency correlation weight value is positively correlated with the current operating frequency.

[0066] Specifically, the frequency-related weight value is a scalar coefficient used to dynamically adjust the relative importance of the rate feature sequence based on the current operating frequency of the RF signal when constructing composite features. This step aims to transform the physical laws of sensor response (skin effect) into a mathematical weighting strategy, allowing the algorithm to focus more on rapidly changing features caused by surface thermal effects during high-frequency measurements. This weight value is calculated using the following formula: in, This represents the frequency-related weight value. This indicates the current operating frequency, which is the current test radio frequency signal frequency set by the user or commanded by the system. The skin depth factor is a factor related to frequency. Related functions are used to characterize the degree of influence of the skin effect, typically It can be represented as =1 / The higher the frequency, the shallower the skin depth, and the smaller the factor value. Q represents the energy balance factor, a normalization constant used to balance the magnitudes of amplitude and rate characteristics. Specifically, it can be calculated using data obtained during the calibration phase: based on a pre-stored standard response library, the typical amplitude level of the standard amplitude characteristic sequence at all standard frequencies (obtained by averaging the absolute values ​​of all elements in the standard amplitude characteristic sequence) is calculated, along with the typical amplitude level of the standard rate characteristic sequence at all standard frequencies (obtained by averaging the absolute values ​​of all elements in the standard rate characteristic sequence). The ratio obtained by dividing the former by the latter is determined as the energy balance factor, which is determined and fixed during the sensor's factory calibration. It is a very small positive number, which can be 10 to the power of negative 5, used to prevent numerical calculation problems caused by the denominator of the formula being zero or too small.

[0067] The above formula dynamically generates weights based on the physical model. The skin depth factor in the denominator... This reflects the effect of frequency on thermal response: frequency The higher, The smaller the value, the smaller the overall denominator, thus affecting the weight value. Increase. This means that at high frequencies, the weight of the rate feature in the composite feature is significantly increased. Energy balance factor Used for global adjustment to ensure that the numerical range of the weight calculation results is reasonable. This ensures the mathematical robustness of the formula across all operating frequency bands (including near DC).

[0068] S302. Perform a weighted calculation on each element in the rate feature sequence based on the frequency-related weight value.

[0069] Furthermore, this step aims to apply the weights calculated in the previous step, reflecting the influence of frequency, to the rate feature sequence characterizing the rate of change in the thermal response, thereby mathematically amplifying or suppressing the importance of this feature. The specific operation is scalar multiplication: let the original rate feature sequence be... Where N is the sequence length, and its value is related to the amplitude feature sequence. The lengths are the same (i.e., consistent with the number of response segment sampling points defined in S101). Weighted calculations generate new sequences. Each of its elements .in, This represents the value of the i-th element in the weighted rate feature sequence. Represents the original rate feature sequence The value of the i-th element.

[0070] S303. Combine the weighted rate feature sequence with the amplitude feature sequence to obtain a composite feature vector.

[0071] Finally, in order to construct a high-dimensional feature that can simultaneously characterize the "static shape" and "dynamic changes" of the thermal response waveform, and to provide comprehensive input information for subsequent accurate pattern matching, the specific implementation process of this step is as follows: First, let the amplitude feature sequence be... The weighted rate feature sequence is They are combined into a composite feature vector by vector concatenation. Its mathematical expression is as follows: in, The composite feature vector is a column vector with a dimension of 2N×1. This represents the amplitude feature sequence, which constitutes the first N elements of the composite feature vector. This represents the weighted rate feature sequence, which constitutes the last N elements of the composite feature vector. This represents the transpose of a vector, explicitly stated here. It is a column vector.

[0072] The formula above shows that the two sequences are combined via vector concatenation. That is, all N elements of the amplitude feature sequence are used as the upper half, and all N elements of the weighted rate feature sequence are used as the lower half, stacked together to form a new vector of length 2N. This new vector... The first half encodes the geometric shape of the waveform, and the second half encodes the transient rate of change after frequency modulation, thus comprehensively characterizing the core dynamic characteristics of the thermal response process.

[0073] Based on the above technical solution, this embodiment of the invention dynamically calculates and applies frequency-related weights according to the current operating frequency, adaptively modulates the rate feature sequence characterizing the speed of thermal response change, and combines it with the amplitude feature sequence characterizing the waveform geometry to construct a composite feature vector that can simultaneously and frequency-optimized characterize the essential characteristics of thermal response "morphology" and "transient change". Thus, by transforming the physical law that "the higher the frequency, the more significant the skin effect, and the more important the initial rate of change of thermal response" into specific mathematical weighting and feature fusion operations, the constructed features have stronger discriminative power and sensitivity when facing different test frequencies and subtle distortions in thermal response caused by frequency changes or device aging. This lays a reliable feature foundation for subsequent high-precision waveform matching and error correction.

[0074] For example, in another temperature compensation method for a thermistor power sensor provided in one embodiment of the present invention, the rate feature sequence is weighted based on the current operating frequency, and the weighted rate feature sequence is combined with the amplitude feature sequence to obtain a composite feature vector. Specifically, the method includes the following steps: S401. Obtain multiple sets of standard frequency response features based on the pre-stored standard response library, and construct a composite reference matrix based on the multiple sets of standard frequency response features.

[0075] The standard response library is a complete set of thermal response data that is pre-established and stored in the sensor's internal memory under a controlled calibration environment before the sensor leaves the factory.

[0076] Optionally, in this step, multiple sets of standard frequency response characteristics are obtained based on a pre-stored standard response library, specifically including the following steps: (1) Obtain the pre-stored standard response library. The standard response library includes complete time-domain thermal response data collected at multiple standard frequencies.

[0077] Specifically, the data in the standard response library is obtained as follows: During the calibration phase, K discrete standard frequency points (e.g., DC, 10GHz, 20GHz, ..., up to the highest operating frequency) covering the sensor's operating frequency band are selected. For each standard frequency point k (k=1,2,...,K), a step radio frequency signal of known power is applied to the sensor, and a high-precision data acquisition system is used to record the power response curve over the entire time span from the moment the power is applied until the sensor temperature reaches complete thermal equilibrium (this process typically lasts several seconds). This complete time-domain power response curve is stored in the library as the standard data for that standard frequency point. Simultaneously, the power value at steady state for each curve is recorded along with the power value at a fixed observation duration (e.g., the same N sampling points as the real-time measurement), and the ratio of the two is calculated to obtain the standard extrapolation factor for that frequency point, which is also stored.

[0078] (2) From the complete time-domain thermal response data corresponding to each standard frequency, extract the segment with the same length as the response segment of the transient power sequence, and perform alignment and normalization to obtain multiple sets of standard amplitude features.

[0079] Specifically, this step aims to extract comparable data segments from the complete standard curve that are aligned with the current real-time observation window in both time and amplitude. For the complete response data at the k-th standard frequency, the first N sampling points are truncated (the same as the response segment length N in the real-time measurement), resulting in an original truncation vector of length N. This truncation vector is then normalized to align its ends and retain only the waveform shape. Specifically, the dynamic range of the truncation vector at the k-th standard frequency is first determined to be significant: its relative dynamic range is calculated. .like Less than the preset second effective signal threshold (the principle for determining its value is the same as that for the first effective signal threshold in real-time data processing). The same, for example, 1×10 can be taken. −7 If the signal is invalid at that standard frequency, its standard amplitude characteristic sequence can be set to zero or it can be excluded from subsequent matching. If the standard amplitude characteristic is greater than or equal to the preset second valid signal threshold, then... The i-th element is calculated using the following formula: in, This represents the value of the i-th sampling point in the standard amplitude feature sequence corresponding to the k-th standard frequency. This represents the power value at the i-th sampling point in the original truncation vector extracted from the complete data at the k-th standard frequency. This represents the power value of the last sampling point (the Nth point) in the cutoff vector of the kth standard frequency, which is the local anchoring value of the standard curve. This represents the average power value of the initial background segment in the complete response data for the k-th standard frequency.

[0080] The above formula performs two normalizations on the standard data. First, the molecule... The amplitude of the entire truncated vector is scaled so that its terminal values ​​become 1, achieving alignment with the real-time data at the end of the observation window. Then, the entire fraction undergoes the exact same normalization operation as step S203 for the real-time data: subtracting the relative baseline value and dividing by the relative dynamic range, ultimately yielding a standard amplitude feature sequence where all elements are in the interval [0,1] and terminal values ​​are strictly equal to 1. Performing this operation on all K standard frequency points yields K sets of standard amplitude features.

[0081] (3) Perform the same difference and time dimension unification processing on each group of standard amplitude characteristics to obtain multiple groups of standard rate characteristics.

[0082] Furthermore, this step aims to calculate the corresponding rate of change for the standard amplitude features to construct standard rate features, ensuring complete consistency with the processing method of real-time features. Specifically, for the k-th group of standard amplitude features, its standard rate feature is calculated according to the same difference and time dimension unification rule as in real-time data processing (S204). For details, please refer to S204 above, which will not be repeated here.

[0083] (4) Weight the multiple sets of standard rate features based on the current operating frequency, and combine the weighted multiple sets of standard rate features with the corresponding multiple sets of standard amplitude features to generate multiple sets of standard frequency response features.

[0084] Finally, the same frequency weighting rule as the real-time features is applied to each set of standard features to construct standard frequency response features that can be used for approximate matching. First, using the current operating frequency, the same frequency-related weight value ω is calculated according to formula S301. Then, this weight value ω is used for each set of standard rate features. We perform weighting to obtain the weighted standard rate characteristic ω× Finally, the standard amplitude characteristics of each group are... Its corresponding weighted standard rate feature ω× Concatenate the components along the dimensional lines to generate the k-th standard frequency response feature ω× Its construction method is similar to that of real-time composite feature vectors. They are exactly the same, meaning the formula types are the same: .

[0085] After the above four sub-steps, multiple sets of standard frequency response characteristics are obtained. A series of 2N-dimensional column vectors (k=1, 2, ..., K) constitute a "feature dictionary" or "base library", where each vector represents a complete mathematical representation (including morphology and weighted rate of change) of the standard dynamic thermal response of the sensor to a specific frequency input under ideal calibration conditions. This is used for subsequent matching and approximation with measured feature vectors that may be distorted.

[0086] Following this, a composite reference matrix is ​​constructed based on multiple sets of standard frequency response characteristics, specifically including: combining the K standard frequency response characteristic vectors generated in the above steps... As column vectors, arranged in order, they form a matrix of dimension 2N×K, which is the composite reference matrix. The mathematical formula is expressed as: .

[0087] The composite reference matrix obtained in this step It is a mathematical structure that organizes the ideal response characteristics at all standard frequencies, and its function is to provide a complete linear spatial basis for subsequent approximation calculations. The measured composite eigenvectors will be expressed as a linear combination of the column vectors of this matrix, and the combination coefficients reflect the degree of matching between the measured waveform and each standard waveform.

[0088] S402. Using the composite eigenvector as the target vector and the composite reference matrix as the basis matrix, the combination coefficients are obtained by solving a linear least squares problem with non-negative constraints.

[0089] Furthermore, this step involves finding an optimal set of weights (combination coefficients) such that the result obtained by linearly combining the weights with the standard basis (composite reference matrix) best approximates the currently measured eigenvectors, which may contain distortions. Specifically, this requires solving for a combination coefficient vector. (Dimension K×1), making as close as possible .

[0090] Due to the non-negativity of the superposition of thermal response energies, the coefficient is required. ≥0. This reduces to solving the following constrained optimization problem: in, The Euclidean norm of a vector. This represents the sum of squares of the elements of a vector. This represents the composite reference matrix, which consists of K standard frequency response eigenvectors. This represents the vector of combined coefficients to be solved, where the k-th element is... The weight corresponding to the k-th standard frequency response feature. Representing vectors all elements All must be greater than or equal to zero.

[0091] The above formula defines a non-negative least squares (NNLS) optimization problem. Objective function The basis matrix was used to measure the performance. With coefficient After linear combination, the target vector The approximation error (sum of squared residuals) must be minimized. Constraints This ensures that the combination coefficients are non-negative, which is consistent with physical meaning. Solving this problem yields a set of optimal non-negative combination coefficients. For example, the Active Set Method can be used to efficiently solve this NNLS problem.

[0092] Based on the above technical solution, this embodiment of the invention dynamically constructs standard frequency response features and composite reference matrices from a pre-stored standard response library, following a process completely consistent with real-time data processing (truncation, alignment, normalization, differencing, frequency weighting, and combination), ensuring that the standard basis and the measured features are in a completely comparable feature space. Furthermore, by solving a non-negative least squares problem, the currently potentially distorted measured features are precisely decomposed and represented as a linear combination of a series of standard feature bases, and quantified combination coefficients are obtained. The advantage of this technique is that it utilizes standard, ideal response patterns as "building blocks" to dynamically fit and interpret actual, condition-affected response waveforms, thus providing a crucial mathematical bridge for subsequently synthesizing high-precision extrapolation factors adapted to the current distortion state based on the combination coefficients, effectively overcoming the shortcomings of fixed lookup table methods in adapting to dynamic deviations.

[0093] For example, such as Figure 2 The diagram shown is an architectural schematic of a temperature compensation system (hereinafter referred to as temperature compensation system 20) for a thermistor power sensor according to an embodiment of the present invention. The temperature compensation system 20 includes: a data acquisition module 21, a feature sequence construction module 22, a composite feature construction module 23, a modal approximation calculation module 24, and a steady-state reconstruction output module 25. The modules are described in detail below: The data acquisition module 21 is used to acquire the transient power sequence generated by the thermistor power sensor under input power excitation within a preset observation period. For details of the process, please refer to S101 above.

[0094] The feature sequence construction module 22 is used to extract the amplitude feature sequence from the transient power sequence and determine the rate feature sequence based on the amplitude feature sequence. The rate feature sequence is used to characterize the rate of change of the thermal response waveform over time. For details, please refer to S102 above.

[0095] The composite feature construction module 23 is used to weight the rate feature sequence based on the current operating frequency, and then combine the weighted rate feature sequence with the amplitude feature sequence to obtain a composite feature vector. This composite feature vector is used to comprehensively characterize the morphology and transient change features of the thermal response waveform. For detailed procedures, please refer to S103 above.

[0096] Modal approximation solution module 24 is used to perform approximation matching calculations between the composite feature vector and multiple sets of standard frequency response features to determine the combination coefficients. These combination coefficients characterize the matching weights between the current thermal response waveform and each standard frequency response waveform. For detailed procedures, please refer to S104 above.

[0097] The steady-state reconstruction output module 25 is used to synthesize multiple preset standard extrapolation factors corresponding to each standard frequency point according to the combination coefficients to obtain a synthesized extrapolation factor applicable to the current operating condition, and to determine the extrapolated steady-state power based on the synthesized extrapolation factor and the transient power sequence. For details of the process, please refer to S105 above.

[0098] It should be noted that the order of the above embodiments of the present invention is merely for descriptive purposes and does not represent the superiority or inferiority of the embodiments. The processes depicted in the accompanying drawings do not necessarily require a specific or sequential order to achieve the desired result. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0099] The various embodiments in this specification are described in a progressive manner. The same or similar parts between the various embodiments can be referred to each other. Each embodiment focuses on describing the differences from other embodiments.

Claims

1. A temperature compensation method for a thermistor power sensor, characterized in that, The method includes: Acquire the transient power sequence generated by the thermistor power sensor under input power excitation within a preset observation period; An amplitude feature sequence is extracted from the transient power sequence, and a rate feature sequence is determined based on the amplitude feature sequence; wherein the rate feature sequence is used to characterize the rate of change of the thermal response waveform over time; The rate feature sequence is weighted based on the current operating frequency, and the weighted rate feature sequence is combined with the amplitude feature sequence to obtain a composite feature vector; wherein, the composite feature vector is used to comprehensively characterize the morphology and transient change characteristics of the thermal response waveform; The composite feature vector is approximated and matched with multiple sets of standard frequency response features to determine the combination coefficients; wherein, the combination coefficients are used to characterize the matching weight between the current thermal response waveform and each standard frequency response waveform; Based on the combination coefficients, multiple standard extrapolation factors corresponding to each standard frequency point are synthesized to obtain a synthesized extrapolation factor applicable to the current operating condition. Based on the synthesized extrapolation factor and the transient power sequence, the extrapolated steady-state power is determined.

2. The temperature compensation method for a thermistor power sensor according to claim 1, characterized in that, The transient power sequence generated by the thermistor power sensor under input power excitation within a preset observation period is obtained, specifically including: The bridge output voltage of the thermistor power sensor is continuously collected; When the rate of change of the bridge output voltage is detected to exceed a preset trigger threshold, a first preset number of sampling points before the corresponding time are extracted to form a background segment, and a second preset number of sampling points after the corresponding time are extracted to form a response segment. The background segment and the response segment are concatenated to form the original voltage sequence, and the original voltage sequence is converted into a power sequence and then smoothed and filtered to obtain the transient power sequence.

3. The temperature compensation method for a thermistor power sensor according to claim 2, characterized in that, Extracting the amplitude feature sequence from the transient power sequence and determining the rate feature sequence based on the amplitude feature sequence specifically includes: Calculate the average power of the background segment in the transient power sequence as the baseline power; Calculate the power value at the end of the sampling point of the response segment in the transient power sequence, and use it as the anchor power; The response segment is normalized based on the transient power sequence, the baseline power, and the anchoring power to obtain the amplitude feature sequence. The amplitude feature sequence is differentially calculated, and the rate feature sequence is determined based on the differential result and the sampling time interval.

4. The temperature compensation method for a thermistor power sensor according to claim 1, characterized in that, The rate feature sequence is weighted based on the current operating frequency, specifically including: Calculate a frequency-related weight value based on the current operating frequency; wherein the frequency-related weight value is positively correlated with the current operating frequency; Each element in the rate feature sequence is weighted according to the frequency-related weight value.

5. The temperature compensation method for a thermistor power sensor according to claim 1, characterized in that, The composite feature vector is approximated and matched with multiple sets of standard frequency response features to determine the combination coefficients, specifically including: The multiple sets of standard frequency response features are obtained based on the pre-stored standard response library, and a composite reference matrix is ​​constructed based on the multiple sets of standard frequency response features. Using the composite eigenvector as the target vector and the composite reference matrix as the basis matrix, the combination coefficients are obtained by solving a linear least squares problem with non-negative constraints.

6. The temperature compensation method for a thermistor power sensor according to claim 5, characterized in that, The multiple sets of standard frequency response features are obtained based on a pre-stored standard response library, specifically including: Obtain a pre-stored standard response library; wherein the standard response library includes complete time-domain thermal response data collected at multiple standard frequencies; From the complete time-domain thermal response data corresponding to each standard frequency, a segment with the same length as the response segment of the transient power sequence is extracted, and after alignment and normalization, multiple sets of standard amplitude features are obtained. Each set of standard amplitude features is subjected to the same difference and time dimension unification processing to obtain multiple sets of standard rate features; The multiple sets of standard rate features are weighted based on the current operating frequency, and the weighted multiple sets of standard rate features are combined with the corresponding multiple sets of standard amplitude features to generate the multiple sets of standard frequency response features.

7. The temperature compensation method for a thermistor power sensor according to claim 1, characterized in that, Based on the combination coefficients, multiple preset standard extrapolation factors corresponding to each standard frequency point are synthesized to obtain a synthesized extrapolation factor applicable to the current operating condition, specifically including: If the result of the approximation matching calculation meets the preset fitting quality condition, the composite extrapolation factor is calculated by weighting the preset multiple standard extrapolation factors according to the combination coefficient. If the result of the approximation matching calculation does not meet the preset fitting quality conditions, the corresponding factor is found from the preset multiple standard extrapolation factors according to the current working frequency, and used as the synthetic extrapolation factor.

8. The temperature compensation method for a thermistor power sensor according to claim 3, characterized in that, Based on the synthetic extrapolation factor and the transient power sequence, the extrapolated steady-state power is determined, specifically including: Obtain the anchoring power and the baseline power determined based on the transient power sequence, and calculate the steady-state power value without environmental correction based on the anchoring power, the baseline power and the synthetic extrapolation factor; The current ambient base temperature is obtained, and the uncorrected steady-state power value is compensated based on the ambient base temperature, the pre-stored reference temperature, and the temperature sensitivity coefficient to obtain the extrapolated steady-state power.

9. The temperature compensation method for a thermistor power sensor according to any one of claims 1-8, characterized in that, The pre-stored standard response library and multiple preset standard extrapolation factors are obtained by applying input power at multiple standard frequencies to the thermistor power sensor under a calibration environment and recording the complete steady-state thermal response process.

10. A temperature compensation system for a thermistor power sensor, characterized in that, The system includes: The data acquisition module is used to acquire the transient power sequence generated by the thermistor power sensor under input power excitation within a preset observation period; A feature sequence construction module is used to extract an amplitude feature sequence from the transient power sequence and determine a rate feature sequence based on the amplitude feature sequence; wherein, the rate feature sequence is used to characterize the rate of change of the thermal response waveform over time; A composite feature construction module is used to weight the rate feature sequence based on the current operating frequency, and combine the weighted rate feature sequence with the amplitude feature sequence to obtain a composite feature vector; wherein, the composite feature vector is used to comprehensively characterize the morphology and transient change features of the thermal response waveform; The modal approximation solution module is used to perform approximation matching calculations between the composite feature vector and multiple sets of standard frequency response features to determine the combination coefficients; wherein, the combination coefficients are used to characterize the matching weights between the current thermal response waveform and each standard frequency response waveform; The steady-state reconstruction output module is used to synthesize multiple preset standard extrapolation factors corresponding to each standard frequency point according to the combination coefficients to obtain a synthesized extrapolation factor applicable to the current operating condition, and to determine the extrapolated steady-state power according to the synthesized extrapolation factor and the transient power sequence.

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