A multi-point calibration method based on pulse oscillation system error

Abstract

The present application belongs to the technical field of forced oscillation, and provides a multi-point calibration method based on system error of pulse oscillation technology, comprising: theoretical impedance data calculation, fitting data collection, compensation surface fitting model construction and impedance data correction; the present application improves the measurement accuracy in the high frequency and high impedance range by constructing the compensation surface fitting model, can process the error caused by factors such as system asymmetry, can realize more accurate calibration for the full frequency band and various impedance ranges, and can also adapt to the physiological conditions of different patients, ensuring the reliability of the measurement results.

Description

Technical Field

[0001] This invention relates to the field of forced oscillation technology, and in particular to a multi-point calibration method for system errors based on pulse oscillation technology. Background Technology

[0002] Forced oscillation (FOO) is a non-invasive method for measuring respiratory mechanics, widely used to assess airway resistance, compliance, and other physiological characteristics. By applying a high-frequency oscillatory pressure signal to the respiratory system and measuring the system's response, FOODS can calculate impedance characteristics at different frequencies. Its principle is based on system identification theory, using the known relationship between the excitation signal and the system response to deduce the airway impedance characteristics. This technique not only aids in diagnosing respiratory diseases but also provides more detailed respiratory mechanics data. However, due to the potential influence of equipment system errors, sensor nonlinear responses, signal noise, and other factors during measurement, ensuring high-precision measurement results under various interference factors is a key challenge in the application of FOODS. Therefore, improving measurement accuracy and effectively reducing system errors are important directions for the further development of this technology. Current limitations: Currently, FOODS widely employs single-point calibration, occlusion calibration, and two-point calibration methods, but each method has its own limitations. Single-point calibration: This is the most common traditional calibration method. In this method, the measuring device is loaded with a known reference impedance, and a correction function is calculated to correlate the measured impedance at each frequency with the reference impedance. While simple to operate, its applicability is limited. The accuracy of the single-point calibration method is only applicable to measurements within the reference impedance range; for high-frequency or high-impedance measurements, it may lead to underestimation, especially at frequencies above 44Hz, where the measurement error increases significantly. The occlusion calibration method: This method simulates a state without any airflow by introducing a system occlusion condition. The system corrects for asymmetry by measuring the impedance under occlusion and comparing it to a known load impedance. Although this method handles system asymmetry well, its complex operation and extremely high sensitivity requirements for the flow measurement system make it difficult to implement in practice. The two-point calibration method: Unlike the single-point calibration method, the two-point calibration method uses two known reference impedances, covering a wider range of measured impedances. Especially at high frequencies, the two-point calibration method offers higher accuracy than the single-point calibration method. This method has lower operational requirements than the occlusion method and avoids extreme occlusion conditions, making it more feasible in practice.

[0003] Technical Challenges and Unmet Needs: Although existing calibration methods have improved the measurement accuracy of forced oscillation technology to some extent, they still face some technical challenges and unmet needs: 1) Complexity of Error Calibration: Existing methods often only provide effective calibration within specific frequency and impedance ranges, making it difficult to handle systematic errors across the entire frequency band and impedance range. This is especially true at high frequencies and in complex airway structures, where traditional methods are not ideal. 2) High Sensitivity Requirements: For example, occlusion methods require highly sensitive flow measurement systems, while single-point calibration methods suffer from insufficient measurement accuracy at high frequencies, leading to difficulties in practical applications. 3) Need to Adapt to Different Clinical Environments: Differences in the physiological characteristics of different patients make it difficult for a single calibration method to cope with various clinical environments, especially in certain special groups, where existing calibration methods struggle to provide ideal accuracy. Summary of the Invention

[0004] In order to overcome the shortcomings of the existing technology, the purpose of this invention is to provide a multi-point calibration method for system errors based on pulse oscillation technology, which solves the problems of small error correction range, poor measurement accuracy and poor adaptability to different environmental requirements of traditional methods.

[0005] To achieve the above objectives, the present invention provides the following solution:

[0006] A multi-point calibration method for system errors based on pulse oscillation technology includes:

[0007] The theoretical impedance values ​​of the target device at various frequencies are calculated using ideal physical models and theoretical formulas to obtain theoretical impedance data.

[0008] The amplitude-frequency compensation coefficient and phase-frequency compensation coefficient are calculated using actual measured impedance and theoretical impedance data at several discrete reference frequency points to obtain fitting data; the fitting data is used to characterize the error characteristics of the system at finite frequency points.

[0009] Construct a system frequency response function, use the fitted data as input to solve for the optimal parameter values ​​using a numerical fitting algorithm, update the system frequency response function with the optimal parameter values, and obtain a continuous compensation surface fitting model;

[0010] The impedance data are corrected using the aforementioned compensation surface fitting model to obtain the correction results.

[0011] Preferably, the theoretical impedance values ​​of the target device at various frequencies are calculated using an ideal physical model and theoretical formulas to obtain theoretical impedance data, including:

[0012] Construct the ideal physical model; the expression of the ideal physical model is: Among them, when hour, , ;when hour, , When 2 hour, for and linear interpolation, for and Linear interpolation; ; This is the total impedance; For screen resistance; The real number that introduces resistance at the connection of the screen pipe; for ; The imaginary unit; Angular frequency; The inner radius of the pipe; This is a scalar value obtained by dividing the gas viscosity by the fluid density; A is the pipe length; A is the pipe cross-sectional area; For gas viscosity; For fluid density; for =2 The value; for =30 hours The value; for =2 The value; for =30 hours The value;

[0013] The theoretical impedance data are determined using the theoretical model.

[0014] Preferably, the amplitude-frequency compensation coefficient and phase-frequency compensation coefficient are calculated at several discrete reference frequency points using actual measured impedance and the theoretical impedance data to obtain fitting data; the fitting data is used to characterize the error characteristics of the system at a finite number of frequency points, including:

[0015] Measure the magnitude of the target impedance at 0Hz to obtain the X data;

[0016] Set the target frequency band range, select discrete frequency points at fixed frequency intervals, and obtain Y data;

[0017] Calculate the amplitude-frequency compensation coefficient and phase-frequency compensation coefficient of the target impedance to obtain Z data; the expression for the amplitude-frequency compensation coefficient is: The expression for the phase frequency compensation coefficient is: ;in, , These are the amplitude frequency compensation coefficient and the phase frequency compensation coefficient, respectively; , These are the actual impedance and the theoretical impedance, respectively.

[0018] The fitted data is obtained by integrating the X data, the Y data, and the Z data.

[0019] Preferably, a system frequency response function is constructed, and the optimal parameter values ​​are obtained by using the fitted data as input through a numerical fitting algorithm. The optimal parameter values ​​are then updated to the system frequency response function to obtain a continuous compensation surface fitting model, including:

[0020] Construct the original system frequency response formula; the expression of the original system frequency response formula is: ;in, The system frequency response function is defined as the system frequency response function at frequency f. For proportional gain; The imaginary unit; For frequency variables; The differential time constant;

[0021] Define the amplitude correction factor; the expression for the amplitude correction factor is: ;in, The amplitude correction coefficient is mentioned above; The target amplitude; For reference frequency;

[0022] The original system frequency response formula is corrected using the amplitude correction coefficient to obtain the corrected system frequency response formula; the expression of the corrected system frequency response formula is: ;in, To utilize the amplitude correction coefficient for An ideal system model after global adjustments;

[0023] The output of the frequency response formula of the correction system is nonlinearly interpolated to obtain the compensation surface fitting model.

[0024] Preferably, the impedance data is corrected using the compensation surface fitting model to obtain the correction result, including:

[0025] Set the amplitude correction coefficient and the phase correction coefficient; the expression for the amplitude correction coefficient is: The expression for the phase correction coefficient is: ;in, , These represent the amplitude correction coefficient and the phase correction coefficient, respectively. , These represent the frequency and the measured impedance magnitude, respectively. , These represent the linear component and offset in amplitude and phase correction, respectively; , These represent the nonlinear component and offset in amplitude correction, respectively.

[0026] An impedance correction formula is constructed based on the amplitude frequency correction coefficient and the phase frequency correction coefficient; the expression of the impedance correction formula is: ;in, For the estimation of the true value of complex impedance; This is the original complex impedance value; The impedance magnitude of the target at 0Hz;

[0027] The impedance correction formula is calculated based on the compensation surface fitting model to obtain the correction result.

[0028] The present invention discloses the following technical effects:

[0029] This invention provides a multi-point calibration method for system errors based on pulse oscillation technology. By constructing a compensation surface fitting model, it solves the problems of small error correction range, poor measurement accuracy, and poor adaptability to different environmental requirements in traditional methods, and achieves accurate calibration of measurement data. Attached Figure Description

[0030] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments 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.

[0031] Figure 1 This is a schematic diagram of a multi-point calibration process for system errors based on pulse oscillation technology provided in an embodiment of the present invention;

[0032] Figure 2 A schematic diagram of the phase compensation surface for system errors based on pulse oscillation technology provided in an embodiment of the present invention;

[0033] Figure 3 A schematic diagram of the amplitude compensation surface for system errors based on pulse oscillation technology provided in an embodiment of the present invention;

[0034] Figure 4 This invention provides a Bland-Altman plot comparing the original impedance value of a device with a known impedance value to a reference value, as shown in the embodiments of the present invention.

[0035] Figure 5 The Bland-Altman plot of the corrected impedance value of a device with known impedance and the reference value is provided for embodiments of the present invention. Detailed Implementation

[0036] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0037] The purpose of this invention is to provide a multi-point calibration method for system errors based on pulse oscillation technology, which solves the problems of small error correction range, poor measurement accuracy, and poor adaptability to different environmental requirements in traditional methods.

[0038] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0039] Figure 1 This is a schematic diagram of a multi-point calibration process for system errors based on pulse oscillation technology provided in an embodiment of the present invention, as shown below. Figure 1 As shown, this invention provides a multi-point calibration method for system errors based on pulse oscillation technology, comprising:

[0040] Step 100: Calculate the theoretical impedance values ​​of the target device at various frequencies using an ideal physical model and theoretical formulas to obtain theoretical impedance data;

[0041] Step 200: Calculate the amplitude-frequency compensation coefficient and phase-frequency compensation coefficient at several discrete reference frequency points using actual measured impedance and the theoretical impedance data to obtain fitting data; the fitting data is used to characterize the error characteristics of the system at finite frequency points.

[0042] Step 300: Construct the system frequency response function, use the fitted data as input to solve for the optimal parameter values ​​through a numerical fitting algorithm, update the optimal parameter values ​​to the system frequency response function, and obtain a continuous compensation surface fitting model;

[0043] Step 400: Use the compensation surface fitting model to correct the impedance data and obtain the correction result.

[0044] Specifically, the theoretical impedance values ​​of the target device at various frequencies are calculated using ideal physical models and theoretical formulas to obtain theoretical impedance data, including:

[0045] Construct the ideal physical model; the expression of the ideal physical model is: Among them, when hour, , ;when hour, , When 2 hour, for and linear interpolation, for and Linear interpolation; ; This is the total impedance; For screen resistance; The real number that introduces resistance at the connection of the screen pipe; for ; The imaginary unit; Angular frequency; The inner radius of the pipe; This is a scalar value obtained by dividing the gas viscosity by the fluid density; A is the pipe length; A is the pipe cross-sectional area; For gas viscosity; For fluid density; for =2 The value; for =30 hours The value; for =2 The value; for =30 hours The value;

[0046] The theoretical impedance data are determined using the theoretical model.

[0047] Furthermore, at several discrete reference frequency points, the amplitude-frequency compensation coefficient and phase-frequency compensation coefficient are calculated using actual measured impedance and the theoretical impedance data to obtain fitting data; the fitting data is used to characterize the error characteristics of the system at a finite number of frequency points, including:

[0048] Measure the magnitude of the target impedance at 0Hz to obtain the X data;

[0049] Set the target frequency band range, select discrete frequency points at fixed frequency intervals, and obtain Y data;

[0050] Calculate the amplitude-frequency compensation coefficient and phase-frequency compensation coefficient of the target impedance to obtain Z data; the expression for the amplitude-frequency compensation coefficient is: The expression for the phase frequency compensation coefficient is: ;in, , These are the amplitude frequency compensation coefficient and the phase frequency compensation coefficient, respectively; , These are the actual impedance and the theoretical impedance, respectively.

[0051] The fitted data is obtained by integrating the X data, the Y data, and the Z data.

[0052] Specifically, a system frequency response function is constructed, and the optimal parameter values ​​are obtained by using the fitted data as input through a numerical fitting algorithm. The optimal parameter values ​​are then updated to the system frequency response function to obtain a continuous compensation surface fitting model, including:

[0053] Construct the original system frequency response formula; the expression of the original system frequency response formula is: ;in, The system frequency response function is defined as the system frequency response function at frequency f. For proportional gain; The imaginary unit; For frequency variables; The differential time constant;

[0054] Define the amplitude correction factor; the expression for the amplitude correction factor is: ;in, The amplitude correction coefficient is mentioned above; The target amplitude; For reference frequency;

[0055] The original system frequency response formula is corrected using the amplitude correction coefficient to obtain the corrected system frequency response formula; the expression of the corrected system frequency response formula is: ;in, To utilize the amplitude correction coefficient for An ideal system model after global adjustments;

[0056] The output of the frequency response formula of the correction system is nonlinearly interpolated to obtain the compensation surface fitting model.

[0057] Furthermore, the impedance data is corrected using the aforementioned compensation surface fitting model to obtain the correction result, including:

[0058] Set the amplitude correction coefficient and the phase correction coefficient; the expression for the amplitude correction coefficient is: The expression for the phase correction coefficient is: ;in, , These represent the amplitude correction coefficient and the phase correction coefficient, respectively. , These represent the frequency and the measured impedance magnitude, respectively. , These represent the linear component and offset in amplitude and phase correction, respectively; , These represent the nonlinear component and offset in amplitude correction, respectively.

[0059] An impedance correction formula is constructed based on the amplitude frequency correction coefficient and the phase frequency correction coefficient; the expression of the impedance correction formula is: ;in, For the estimation of the true value of complex impedance; This is the original complex impedance value; The impedance magnitude of the target at 0Hz;

[0060] The impedance correction formula is calculated based on the compensation surface fitting model to obtain the correction result.

[0061] Specifically, the method involves forced oscillation techniques, where errors primarily manifest as amplitude and phase errors. Since impedance measurements are influenced by frequency and impedance range, different measurement points can lead to variations in error. To achieve accurate error correction across multiple frequencies and impedance ranges, this method designs a multi-point calibration surface, fitting amplitude-frequency and phase-frequency compensation surfaces respectively. These calibration surfaces can be applied at different frequencies and impedances to achieve accurate correction of impedance data measured using forced oscillation techniques. The key steps are as follows:

[0062] S1: Theoretical calculation of reference impedance value:

[0063] Taking the standard 0.2 impedance provided by Rudolf as an example, each impedance is... The impedance is determined by its real part ( ) and imaginary part ( The impedance is composed of a screen on its front side and a short tube, where the screen will affect the impedance. The short tube introduces impedance Correction requires knowing the true value of the impedance to compare with the measured impedance value and obtain the correction function. Theoretical impedance model for a screen-pipe system:

[0064]

[0065] in, This is the total impedance; For screen resistance; .

[0066] and The theoretical calculation method uses dimensionless coefficients because the airflow patterns differ at different vibration frequencies. Evaluate:

[0067]

[0068] Angular frequency, The inner radius of the pipe, Let A be the pipe length, A be the pipe cross-sectional area, and v be the kinematic viscosity of the fluid. This has been verified.

[0069]

[0070]

[0071] When 2 time and They are respectively and , and The interpolation; A is the cross-sectional area of ​​the cylinder. Let n be the fluid density, and n be the coefficient of L at different frequencies. This is the derivation of the coefficients.

[0072] hour Derivation of: Inertial drag The formula originates from the cylinder's cross-sectional area A, with gas pressures P1 and P2 at the two ends of the cylinder. According to Newton's second law, for the gas inside the cylinder:

[0073]

[0074] Where A is the fluid acceleration; A is the cross-sectional area of ​​the cylinder. For speed, The fluid density is given.

[0075] Therefore, the air pressure at both ends of the pipe have:

[0076]

[0077] in V(t) is the volume of the fluid as a function of time; Let be the fluid velocity, and be the derivative of the fluid volume with respect to time. Let be the fluid acceleration, and be the derivative of the fluid velocity with respect to time.

[0078] Furthermore, experiments have shown that when When this is the case, it is recommended that L be valued as follows: .

[0079] S2: Reference Figure 2 and Figure 3 Data preparation for fitting:

[0080] X data: The magnitude of the actual measured impedance at 0Hz, used to determine the measurement error under different impedances.

[0081] Y data: Target frequency, used to determine measurement error at different frequencies.

[0082] Z-data: Amplitude compensation coefficient and phase compensation coefficient, used to calibrate measurement errors.

[0083] Amplitude correction coefficient That is, by calculating the ratio of the actual impedance amplitude to the theoretical impedance magnitude, the amplitude correction coefficient is obtained.

[0084] Phase correction coefficient: That is, by calculating the difference between the actual impedance phase and the theoretical impedance phase, the phase correction coefficient is obtained.

[0085] S3: Reference Figure 2 and Figure 3 Construction of the compensation surface fitting model:

[0086] To fit the frequency response of the actual impedance data, the system transfer function is used to calculate the amplitude and phase frequency compensation surfaces. The system frequency response is:

[0087]

[0088] Its amplitude characteristics are:

[0089]

[0090] To meet specific frequency The amplitude design requirements at the location define the amplitude correction coefficient. ,satisfy:

[0091]

[0092] in, To represent the frequency response function (complex form) of the system at frequency f; The proportional gain of the system; The imaginary unit; It is a frequency variable, and the unit is usually Hertz (Hz); The system's differential time constant; To design the target amplitude; For design reference frequency.

[0093] Transfer function after amplitude correction Represented as:

[0094]

[0095] The model uses a quadratic function to obtain the relationship between the amplitude compensation coefficient and the impedance, and uses the amplitude-frequency response function to obtain the amplitude compensation coefficient. Relationship with frequency:

[0096]

[0097] Where x is the frequency and y is the magnitude of the measured impedance. , , , These are constant coefficients. The fitting model will optimize the fitting parameters using a nonlinear least squares method to accurately fit the amplitude compensation coefficients.

[0098] Corresponding phase response for:

[0099]

[0100] This phase reflects the time delay properties of the controller for different frequency components of the input signal, therefore the frequency response phase... for:

[0101]

[0102] in, , These are the time constants of the first-order lag element and the first-order lead element, respectively.

[0103] The relationship between the phase compensation coefficient and impedance is obtained using a quadratic function, and the amplitude compensation coefficient is obtained using the phase frequency response function. Relationship with frequency:

[0104]

[0105] This relationship is used to fit the phase frequency compensation coefficients.

[0106] Fitting Algorithm and Optimization: The fitting algorithm uses nonlinear interpolation. By adjusting the initial values ​​and optimization parameters of the fitting parameters, the correction coefficients at each frequency are accurately fitted.

[0107] S4: Read the correction coefficient:

[0108] Read the saved fitting results and apply them to the actual measured impedance data. and The computer equipment uses correction factors to correct the amplitude and phase of the measured impedance, thus obtaining updated corrected impedance data. For each measurement pulse, the computer equipment calculates the measured impedance value and uses the previously obtained correction factors (…). , The impedance data is corrected using the following formula:

[0109]

[0110] in, This is the true value estimate of the complex impedance of the target under test obtained after correction by the aforementioned compensated surface fitting model; The original complex impedance value, including systematic errors, is obtained directly from the measurement system. The impedance magnitude of the target at 0Hz; This represents the frequency of the signal.

[0111] The beneficial effects of this invention are as follows:

[0112] This invention improves measurement accuracy in high-frequency and high-impedance ranges by constructing a compensated surface fitting model. It can handle errors caused by factors such as system asymmetry, achieve more accurate calibration across the entire frequency band and multiple impedance ranges, and adapt to the physiological conditions of different patients, ensuring the reliability of measurement results.

[0113] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0114] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A multi-point calibration method for system errors based on pulse oscillation technology, characterized in that, include: The theoretical impedance values ​​of the target device at various frequencies are calculated using ideal physical models and theoretical formulas to obtain theoretical impedance data. The amplitude-frequency compensation coefficient and phase-frequency compensation coefficient are calculated using actual measured impedance and theoretical impedance data at several discrete reference frequency points to obtain fitting data; the fitting data is used to characterize the error characteristics of the system at finite frequency points. Construct a system frequency response function, use the fitted data as input to solve for the optimal parameter values ​​using a numerical fitting algorithm, update the system frequency response function with the optimal parameter values, and obtain a continuous compensation surface fitting model; The impedance data is corrected using the aforementioned compensation surface fitting model to obtain the correction result; Constructing a system frequency response function, using the fitted data as input, and solving for the optimal parameter values ​​using a numerical fitting algorithm, then updating the system frequency response function with the optimal parameter values ​​to obtain a continuous compensated surface fitting model, including: Construct the original system frequency response formula; the expression of the original system frequency response formula is: ;in, The system frequency response function is defined as the system frequency response function at frequency f. For proportional gain; The imaginary unit; For frequency variables; The differential time constant; Define the amplitude correction factor; the expression for the amplitude correction factor is: ;in, The amplitude correction coefficient is mentioned above; The target amplitude; For reference frequency; The original system frequency response formula is corrected using the amplitude correction coefficient to obtain the corrected system frequency response formula; the expression of the corrected system frequency response formula is: ;in, To utilize the amplitude correction coefficient for An ideal system model after global adjustments; The output of the frequency response formula of the correction system is nonlinearly interpolated to obtain the compensation surface fitting model.

2. The multi-point calibration method for system errors based on pulse oscillation technology according to claim 1, characterized in that, The theoretical impedance values ​​of the target device at various frequencies are calculated using an ideal physical model and theoretical formulas, yielding theoretical impedance data, including: Construct the ideal physical model; the expression of the ideal physical model is: Among them, when hour, , ;when hour, , When 2 hour, for and linear interpolation, for and Linear interpolation; ; This is the total impedance; For screen resistance; The real number that introduces resistance at the connection of the screen pipe; for ; The imaginary unit; Angular frequency; The inner radius of the pipe; This is a scalar value obtained by dividing the gas viscosity by the fluid density; A is the pipe length; A is the pipe cross-sectional area; Gas viscosity; For fluid density; for =2 The value; for =30 hours The value; for =2 The value; for =30 hours The value; The theoretical impedance data are determined using the ideal physical model.

3. The multi-point calibration method for system errors based on pulse oscillation technology according to claim 2, characterized in that, The amplitude frequency compensation coefficient and phase frequency compensation coefficient are calculated using actual measured impedance and theoretical impedance data at several discrete reference frequency points to obtain fitting data; The fitted data is used to characterize the error characteristics of the system at a finite frequency point, including: Measure the magnitude of the target impedance at 0Hz to obtain the X data; Set the target frequency band range, select discrete frequency points at fixed frequency intervals, and obtain Y data; Calculate the amplitude-frequency compensation coefficient and phase-frequency compensation coefficient of the target impedance to obtain Z data; the expression for the amplitude-frequency compensation coefficient is: The expression for the phase frequency compensation coefficient is: ;in, , These are the amplitude frequency compensation coefficient and the phase frequency compensation coefficient, respectively; , These are the actual impedance and the theoretical impedance, respectively. The fitted data is obtained by integrating the X data, the Y data, and the Z data.

4. The multi-point calibration method for system errors based on pulse oscillation technology according to claim 3, characterized in that, The impedance data is corrected using the aforementioned compensation surface fitting model to obtain the correction results, including: Set the amplitude correction coefficient and the phase correction coefficient; the expression for the amplitude correction coefficient is: The expression for the phase correction coefficient is: ;in, , These represent the amplitude correction coefficient and the phase correction coefficient, respectively. , These represent the frequency and the measured impedance magnitude, respectively. , These represent the linear component and offset in amplitude and phase correction, respectively; , These represent the nonlinear component and offset in amplitude correction, respectively. An impedance correction formula is constructed based on the amplitude correction coefficient and the phase correction coefficient; the expression of the impedance correction formula is: ;in, For the estimation of the true value of complex impedance; This is the original complex impedance value; The impedance magnitude of the target at 0Hz; The impedance correction formula is calculated based on the compensation surface fitting model to obtain the correction result.

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