Pulse eddy current receiving system parameter identification and real-time calibration method based on underdamping dynamic response

Abstract

The invention relates to a pulse eddy current receiving system parameter identification and real-time calibration method based on an under-damping dynamic response, and belongs to the technical field of pulse eddy current. When coil calibration is carried out, a state switching switch S is switched to the end 1, a damping resistor Rb and a state switching resistor R1 are connected in series to serve as a matching resistor, and an under-damping state is formed; meanwhile, a receiving coil applies a linearly changing excitation signal, a step signal epsilon (t) is generated in the receiving coil, signals at the two ends of the coil are collected, peak time, overshoot and a first system response steady-state value are extracted, and therefore the natural frequency and the damping ratio are calculated; similarly, a second system response steady-state value is extracted, and the equivalent resistance R0 of the receiving coil is calculated; obtaining a mapping relation among the natural frequency, the damping ratio, the inductance L of the receiving coil and the distributed capacitance C; and alternately optimizing the double nonlinear equations based on a parameter identification method, setting a target function based on the double linear equations, and carrying out parameter identification on L and C.

Description

Technical Field

[0001] The invention belongs to the technical field of pulse eddy current technology and relates to a method for parameter identification and real-time calibration of a pulse eddy current receiving system based on underdamped dynamic response. Background Art

[0002] The pulsed eddy current receives the secondary magnetic field generated by the eddy current of the object to be detected through the receiving coil. The secondary magnetic field is converted into an induced voltage through the coil induction. The process of converting to the induced voltage is lossless. After the induced voltage passes through the coil and the acquisition system, its attenuation law will be affected by the transition process of the receiving coil. The attenuation law of the induced voltage signal finally obtained is inconsistent with the theoretical curve. In order to eliminate the influence of the coil transition process on the measurement signal and improve the accuracy of the magnetic field detection signal, the coil parameters are usually measured to obtain its transfer function, and then the induced voltage signal is eliminated by deconvolution to restore the induced electromotive force. In the process of inverse operation, the accuracy of the coil parameters determines the accuracy of the operation results and the accuracy of the signal inversion imaging. After the initial measurement of the coil, due to the influence of factors such as the operating time and the operating environment, the coil parameters will change, and the calibration of the received signal will deviate from the actual result. However, since the receiving system is generally an integrated packaging design, it is difficult to measure the coil parameters by the method of leading out the receiving coil port.

[0003] In order to accurately measure the secondary field response through the distorted receiving coil output signal, it is necessary to establish a mapping between the coil induced electromotive force and the output signal. This process is called the calibration of the coil sensor. For coil sensors, the commonly used calibration method is to establish a controllable calibration magnetic field in space, and solve the calibration file of the coil by analyzing the relationship between the coil induced electromotive force ε(t) and its output signal u(t). In order to analyze the law of input and output signals, a sinusoidal signal is usually used as the calibration signal, and several frequency values ​​are selected within the frequency range under investigation. The amplitude and phase angle values ​​of the input and steady-state output signals at each calibration frequency are measured respectively. The transfer function of the coil to be tested is obtained by fitting the experimental data, which is called the frequency response method. However, the environmental medium or structural deformation will have an impact on the calibration file that cannot be ignored, and the calibration work of the transient electromagnetic receiving system is not a one-time thing.

[0004] The frequency response test method is a classic calibration method for coil sensors. It obtains the coil induced electromotive force ε(t) and its output signal u(t) by establishing a controllable calibration magnetic field in space, and obtains the calibration file of the coil to be tested by fitting the experimental data. In the frequency response method, the induced electromotive force ε(t) of the coil to be tested needs to be solved according to Faraday's law of electromagnetic induction. To ensure the controllability of ε(t), this method not only requires a high-precision signal generator, but also must ensure the uniformity of the calibration magnetic field, which places high demands on the field source; the equipment used to generate a uniform magnetic field must be designed according to the size of the coil to be tested, and has poor versatility, and cannot achieve on-site calibration of the device.

[0005] In summary, the pulsed eddy current receiving coil will cause parameter changes due to long-term operation and the operating environment, which will lead to signal calibration deviation. Summary of the invention

[0006] In view of this, an object of the present invention is to provide a method for parameter identification and real-time calibration of a pulsed eddy current receiving system based on underdamped dynamic response.

[0007] In order to achieve the above object, the present invention provides the following technical solutions:

[0008] A method for parameter identification and real-time calibration of a pulsed eddy current receiving system based on underdamped dynamic response comprises the following steps:

[0009] S1: In normal operation, the state switch S is connected to the 0 terminal, and the damping resistor R b Connected to both ends of the receiving coil as a matching resistor, it is used to make the pulse eddy current receiving system in a critical damping state or a slightly over-damped state;

[0010] S2: When the coil is calibrated, the state switch S is switched from the 0 end to the 1 end, and the damping resistor R b It is connected in series with the state switching resistor R1 as a matching resistor to form an underdamped state; at the same time, a linearly varying excitation signal is applied to the receiving coil to generate a step signal ε(t) in the receiving coil, and the signals at both ends of the coil are collected to extract the peak time, overshoot and the first system response steady-state value, thereby calculating the natural frequency and damping ratio;

[0011] Switch the state switch S to terminal 2, and set the damping resistor R b It is connected in series with the state switching resistor R2 as a matching resistor to form an underdamped state; at the same time, a linearly varying excitation signal is applied to the receiving coil to generate a step signal ε(t) in the receiving coil, and the signals at both ends of the coil are collected to extract the steady-state value of the second system response;

[0012] S3: calculating the equivalent resistance R0 of the receiving coil according to the first system response steady-state value and the second system response steady-state value;

[0013] S4: When the natural frequency, damping ratio and R0 are all known, a mapping relationship between the natural frequency, damping ratio and the inductance L and distributed capacitance C of the receiving coil is obtained;

[0014] S5: Based on the parameter identification method, the dual nonlinear equations are alternately optimized, and the objective function based on the dual linear equations is set to perform parameter identification on the inductance L and distributed capacitance C of the receiving coil.

[0015] Furthermore, the damping resistor R b As the matching resistance in normal operation, the calculation formula is as follows:

[0016]

[0017] Among them, R0, L, and C are the equivalent resistance, inductance, and distributed capacitance of the receiving coil, respectively.

[0018] Further, the specific values ​​of the peak time, overshoot and system response steady-state value can be extracted from the signals at both ends of the coil collected in step S2;

[0019] The peak time is the time required for the system response to reach the first maximum value, which is related to the damping ratio ζ1 and the natural frequency ω when the state switching switch S is switched to the 1 end. n1 Related:

[0020]

[0021] The overshoot is the maximum percentage of the step response exceeding the steady-state value, and its magnitude is related to the damping ratio ζ1 when the state switching switch S is switched to the 1 end:

[0022]

[0023] After collecting the specific values ​​of overshoot and peak time, the damping ratio ζ1 and natural frequency ω are calculated using the above formula. n1 The relationship between the steady-state value of the system response and the equivalent resistance and matching resistance of the receiving coil is as follows:

[0024]

[0025] Further, in step S3, according to the first system response steady-state value y collected in step S2 s1 and the second system response steady-state value y s2 , calculate the equivalent resistance R0 of the receiving coil:

[0026] R bn =R b +R n n=1,2

[0027]

[0028] Further, in step S4, at the known natural frequency ω n1 , damping ratio ζ1, R0, R1 and R b In the case of specific values, according to ω n1 , the expression of ζ1:

[0029]

[0030] It can be seen that ω n1 , ζ1 is only related to the inductance L and distributed capacitance C of the receiving coil, thereby establishing a mapping relationship between the natural frequency, damping ratio and the inductance L and distributed capacitance C of the receiving coil.

[0031] Further, step S5 specifically includes the following steps:

[0032] Since the mapping relationship between the natural frequency, damping ratio and the inductance L and distributed capacitance C of the receiving coil is a double nonlinear equation, direct solution is difficult and has large errors. Therefore, the parameter identification method is used to solve the inductance and capacitance parameters of the receiving coil.

[0033] First, when designing the receiving system, the parameters of the receiving coil are measured and the measured values ​​are set as the initial values ​​of the unknown quantities L and C;

[0034] Then, the unknowns are updated alternately, and the dual nonlinear equations are expressed as:

[0035]

[0036] Fix C and solve for L: In the first iteration, use f1 = (L, C) = 0, f2 = (L, C) = 0, and use Newton's method to solve for the new value of L;

[0037] Fix L and solve for C: In the next iteration, use f1 = (L, C) = 0, f2 = (L, C) = 0, and use Newton's method to solve for the value of C;

[0038] Continue to update L and C alternately until the convergence criteria are met;

[0039] In each alternating update process, the residual change is monitored to determine whether the optimization has converged stably;

[0040]

[0041] The error requirement ε is used to limit the number of iterations and adjust the solution accuracy of L and C, thereby realizing the parameter identification of the receiving coil inductance and distributed capacitance.

[0042] The beneficial effect of the present invention is that: the present invention can improve the accuracy of system identification, improve the robustness to model errors and make full use of the advantages of nonlinear optimization on the basis of realizing online identification and real-time calibration of pulsed eddy current receiving system by establishing a method of dual nonlinear identification equations, thereby making parameter identification more reliable. At the same time, compared with the traditional frequency response method, it does not need to establish a controllable calibration magnetic field, and has the advantages of easy operation and wide application range.

[0043] Other advantages, objectives and features of the present invention will be described in the following description to some extent, and to some extent, will be obvious to those skilled in the art based on the following examination and study, or can be taught from the practice of the present invention. The objectives and other advantages of the present invention can be realized and obtained through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention will be described in detail below in conjunction with the accompanying drawings, wherein:

[0045] Figure 1 This is a schematic diagram of receiving coil state switching and signal acquisition;

[0046] Figure 2 The second-order system characteristic analysis, where (a) is the unit step response of the second-order system at different damping ratios, (b) is the step response and characteristic parameters under underdamping, and (c) is the relationship curve between matching resistance and damping ratio;

[0047] Figure 3 Create schematics for parameter mapping;

[0048] Figure 4 Schematic diagram of the whole process of parameter identification. DETAILED DESCRIPTION

[0049] The following describes the embodiments of the present invention by specific examples, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments only illustrate the basic concept of the present invention in a schematic manner, and the following embodiments and features in the embodiments can be combined with each other without conflict.

[0050] It should be noted that the illustrations provided in the following embodiments are only schematic illustrations of the basic concept of the present invention, and thus the drawings only show components related to the present invention rather than being drawn according to the number, shape and size of components in actual implementation. In actual implementation, the type, quantity and proportion of each component may be changed arbitrarily, and the component layout may also be more complicated.

[0051] In the following description, numerous details are discussed to provide a more thorough explanation of the embodiments of the present invention. However, it is obvious to those skilled in the art that the embodiments of the present invention can be implemented without these specific details. In other embodiments, well-known structures and devices are shown in the form of block diagrams rather than in detail to avoid making the embodiments of the present invention difficult to understand.

[0052] The schematic diagram of the receiving coil state switching and signal acquisition designed by the present invention is as follows Figure 1 As shown, R b is the damping matching resistor of the receiving coil, S is the state switching switch, R1 is the state switching resistor, ε(t) is the step signal, V(t) is the induced electromotive force received by the receiving coil, and U(t) is the induced electromotive force measured by the acquisition module.

[0053] During normal operation, the state switching switch S is at the 0 end. At this time, the transfer function, damping ratio and natural frequency of the system are as follows:

[0054] Transfer function:

[0055]

[0056] Natural frequency ω n :

[0057]

[0058] Damping ratio ζ:

[0059]

[0060] Among them, R0, L, C are the equivalent resistance, inductance and distributed capacitance of the receiving coil, and s is the complex variable obtained after Laplace transformation. In order to ensure that the signal output by the sensor minimizes distortion and obtains high-quality output response and relatively flat frequency response, matching resistors can be connected at both ends of the coil to put the system in a critical damping state. However, in actual applications, the matching resistance is usually appropriately increased to make the system work in a slightly over-damped state to avoid oscillation caused by the system becoming under-damped due to uncertain factors. The calculation formula of the matching resistance is as follows:

[0061]

[0062] When the coil is calibrated, the switch is switched from terminal 0 to terminal 1. At this time, the damping matching resistor R b It is connected in series with the state switching resistor R1, and a linearly changing excitation signal is applied to the receiving coil. A step signal ε(t) is generated in the receiving coil, and the acquisition module acquires the signals at both ends of the coil. The system transfer function at this time is:

[0063]

[0064] R b1 =R b +R1

[0065] From the transfer function, we can see that the natural frequency ω of the system is n1 The expression of the damping ratio ζ1 remains unchanged, but because the damping resistor is connected in series with the state switching resistor, the matching resistance of the system increases, and the system is converted from the original critical damping / slightly overdamped state to the underdamped state.

[0066] The unit step response of the second-order system at different damping ratios is as follows: Figure 2 As shown in (a), when the system is in an underdamped state, the system will oscillate, and as the damping ratio decreases, the amplitude of the oscillation increases. The response signal waveform and characteristic parameters under underdamped oscillation are shown in Figure 2 As shown in (b) in the figure, when the system is in an underdamped oscillation state, the step response of the system is oscillatory, the time to reach the peak for the first time is the peak time, and the percentage of the peak value exceeding the steady-state value corresponds to the overshoot. The relationship between the damping ratio and the matching resistance of the system is shown in Figure 2 As shown in (c), increasing the matching resistance value will reduce the damping ratio of the system. Therefore, by controlling the series state switching resistance through the switch, the system can transition from the critical damping state to the underdamped state.

[0067] The present invention is controlled by switch S. When the system is calibrated, the state switching resistor R1 and the damping resistor R b The series connection makes the system underdamped, and the peak time, overshoot and system steady-state value can be collected from the signals at both ends of the coil.

[0068] Peak time is the time required for the system response to reach its first maximum value, which is usually proportional to the damping ratio ζ1 and the natural frequency ω n1 Related:

[0069]

[0070] Overshoot is the maximum percentage by which the step response exceeds the steady-state value. For a second-order system, its magnitude is closely related to the damping ratio ζ.

[0071]

[0072] System steady-state value:

[0073]

[0074] y s is the steady-state value of the system response. It can be seen from the above formula that the steady-state value of the system is only related to the matching resistance and the coil parameter R0. Therefore, R1, R2 and the damping resistance R can be switched by switching the state switch S. b The matching resistors are connected in series to adjust the R0 parameter.

[0075] R bn =R b +R n n=1,2

[0076]

[0077] The two characteristic parameters are only related to the natural frequency and damping ratio, and have nothing to do with the parameters to be identified. n , the natural frequency ω can be established when the damping ratio ζ is specific. n , the mapping relationship between the damping ratio ζ and the parameters to be identified L, C.

[0078] The corresponding parameter mapping diagram is as follows Figure 3 As shown in the figure, after collecting the specific values ​​of overshoot and peak time, firstly, the overshoot and peak time are compared with the damping ratio ζ1 and the natural frequency ω n1 The relationship between the damping ratio ζ1 and the natural frequency ω is calculated n1 Specific values:

[0079]

[0080] Then by:

[0081]

[0082] Under the premise that the specific values ​​of the equivalent resistance and matching resistance of the receiving coil are known, the damping ratio ζ1 and the natural frequency ω n1 Only related to L and C, thus establishing the natural frequency ω n1 , the mapping relationship between the damping ratio ζ1 and the parameters to be identified L, C.

[0083] After establishing the natural frequency ω n1After the dual nonlinear mapping relationship between the damping ratio ζ1 and the parameters to be identified L0, C0 is determined, the dual nonlinear equations are alternately optimized based on the parameter identification method, and the objective function based on the bilinear equation is set to perform parameter identification on the parameters to be identified. Finally, the accuracy of the identification results is evaluated through the system response to obtain the accurate results of L and C after the change, thereby realizing the online identification and real-time calibration technology of the pulsed eddy current receiving system. The corresponding parameter identification flow chart is as follows: Figure 4 shown.

[0084] Specifically, when the natural frequency ω is obtained n1 , the mapping relationship between the damping ratio ζ1 and the parameters to be identified L and C is based on this. Since the equation is a double nonlinear equation, direct solution is difficult and has large errors. Therefore, the parameter identification method is used to solve the inductance and capacitance parameters of the receiving coil.

[0085] First, the parameters of the receiving coil are measured when designing the receiving system. Although the parameters of the receiving coil may deviate during operation, the error is small, so the measured values ​​are set as the initial values ​​of the unknown quantities L and C.

[0086] Then, the unknowns are updated alternately. The dual nonlinear equations are expressed as:

[0087]

[0088] Fix C and solve for L: In the first iteration, use f1=(L,C)=0, f2=(L,C)=0 and use Newton's method to solve for the new value of L.

[0089] Fix L and solve for C: In the next iteration, use f1=(L,C)=0, f2=(L,C)=0 and Newton's method to solve for the value of C.

[0090] Continue to update L and C alternately until the convergence criteria are met.

[0091] During each alternating update process, the residual change is monitored to determine whether the optimization has converged stably.

[0092]

[0093] The error requirement ε is used to limit the number of iterations and adjust the solution accuracy of L and C, thereby realizing the parameter identification of the receiving coil inductance and distributed capacitance.

[0094] By establishing a dual nonlinear identification equation, the accuracy of system identification can be improved, the robustness to model errors can be improved, and the advantages of nonlinear optimization can be fully utilized on the basis of realizing online identification and real-time calibration of the pulsed eddy current receiving system, so that parameter identification is more reliable. At the same time, compared with the traditional frequency response method, it does not require the establishment of a controllable calibration magnetic field, and has the advantages of easy operation and wide application range.

[0095] In the above embodiments, the description's reference to "this embodiment" indicates that a particular feature, structure, or characteristic described in conjunction with the embodiment is included in at least some embodiments, but not necessarily all embodiments. Multiple occurrences of "this embodiment" do not necessarily all refer to the same embodiment.

[0096] In the above-described embodiments, although the invention has been described in conjunction with specific embodiments of the invention, many substitutions, modifications, and variations of these embodiments will be apparent to those of ordinary skill in the art based on the foregoing description. For example, other storage structures (e.g., dynamic RAM (DRAM)) may use the embodiments discussed. Embodiments of the invention are intended to encompass all such substitutions, modifications, and variations that fall within the broad scope of the appended claims.

[0097] This embodiment further provides a computer-readable storage medium on which a computer program is stored. When the program is executed by a processor, any one of the methods in this embodiment is implemented.

[0098] This embodiment also provides an electronic terminal, including: a processor and a memory;

[0099] The memory is used to store a computer program, and the processor is used to execute the computer program stored in the memory, so that the terminal executes any one of the methods in this embodiment.

[0100] The computer-readable storage medium in this embodiment can be understood by ordinary technicians in this field: all or part of the steps of implementing the above-mentioned method embodiments can be completed by hardware related to the computer program. The aforementioned computer program can be stored in a computer-readable storage medium. When the program is executed, the steps of the above-mentioned method embodiments are executed; and the aforementioned storage medium includes: ROM, RAM, magnetic disk or optical disk and other media that can store program codes.

[0101] The electronic terminal provided in this embodiment includes a processor, a memory, a transceiver and a communication interface. The memory and the communication interface are connected to the processor and the transceiver and complete communication with each other. The memory is used to store computer programs, the communication interface is used to communicate, and the processor and the transceiver are used to run computer programs so that the electronic terminal executes each step of the above method.

[0102] In this embodiment, the memory may include a random access memory (RAM), and may also include a non-volatile memory (non-volatile memory), such as at least one disk memory.

[0103] The above-mentioned processor can be a general-purpose processor, including a central processing unit (CPU), a network processor (NP), etc.; it can also be a digital signal processor (DSP), an application specific integrated circuit (ASIC), a field programmable gate array (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components.

[0104] The present invention can be used in many general or special computing system environments or configurations, such as personal computers, server computers, handheld or portable devices, tablet devices, multiprocessor systems, microprocessor-based systems, set-top boxes, programmable consumer electronic devices, network PCs, minicomputers, mainframe computers, distributed computing environments including any of the above systems or devices, and the like.

[0105] The present invention may be described in the general context of computer-executable instructions executed by a computer, such as program modules. Generally, program modules include routines, programs, objects, components, data structures, etc. that perform specific tasks or implement specific abstract data types. The present invention may also be practiced in distributed computing environments where tasks are performed by remote processing devices connected through a communication network. In a distributed computing environment, program modules may be located in local and remote computer storage media, including storage devices.

[0106] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solution of the present invention can be modified or replaced by equivalents without departing from the purpose and scope of the technical solution, which should be included in the scope of the claims of the present invention.

Claims

1. A method for parameter identification and real-time calibration of a pulsed eddy current receiving system based on underdamped dynamic response, characterized in that: The following steps are involved: S1: In normal operation, the state switch S is connected to the 0 terminal, and the damping resistor R b Connected to both ends of the receiving coil as a matching resistor, it is used to make the pulse eddy current receiving system in a critical damping state or a slightly over-damped state; S2: When the coil is calibrated, the state switch S is switched from the 0 end to the 1 end, and the damping resistor R b It is connected in series with the state switching resistor R1 as a matching resistor to form an underdamped state; at the same time, a linearly varying excitation signal is applied to the receiving coil to generate a step signal ε(t) in the receiving coil, and the signals at both ends of the coil are collected to extract the peak time, overshoot and the first system response steady-state value, thereby calculating the natural frequency and damping ratio; Switch the state switch S to terminal 2, and set the damping resistor R b It is connected in series with the state switching resistor R2 as a matching resistor to form an underdamped state; at the same time, a linearly varying excitation signal is applied to the receiving coil to generate a step signal ε(t) in the receiving coil, and the signals at both ends of the coil are collected to extract the steady-state value of the second system response; S3: calculating the equivalent resistance R0 of the receiving coil according to the first system response steady-state value and the second system response steady-state value; S4: When the natural frequency, damping ratio and R0 are all known, a mapping relationship between the natural frequency, damping ratio and the inductance L and distributed capacitance C of the receiving coil is obtained; S5: Based on the parameter identification method, the dual nonlinear equations are alternately optimized, and the objective function based on the dual linear equations is set to perform parameter identification on the inductance L and distributed capacitance C of the receiving coil.

2. The method for parameter identification and real-time calibration of a pulsed eddy current receiving system based on underdamped dynamic response according to claim 1, characterized in that: Damping resistor R b As the matching resistance in normal operation, the calculation formula is as follows: Among them, R0, L, and C are the equivalent resistance, inductance, and distributed capacitance of the receiving coil, respectively.

3. The method for parameter identification and real-time calibration of a pulsed eddy current receiving system based on underdamped dynamic response according to claim 1, characterized in that: The specific values ​​of peak time, overshoot and system response steady-state value can be extracted from the signals collected at both ends of the coil in step S2; The peak time is the time required for the system response to reach the first maximum value, which is related to the damping ratio ζ1 and the natural frequency ω when the state switching switch S is switched to the 1 end. n1 Related: The overshoot is the maximum percentage of the step response exceeding the steady-state value, and its magnitude is related to the damping ratio ζ1 when the state switching switch S is switched to the 1 end: After collecting the specific values ​​of overshoot and peak time, the damping ratio ζ1 and natural frequency ω are calculated using the above formula. n1 ; The relationship between the steady-state value of the system response and the equivalent resistance and matching resistance of the receiving coil is as follows:

4. The method for parameter identification and real-time calibration of a pulsed eddy current receiving system based on underdamped dynamic response according to claim 3 is characterized in that: In step S3, according to the first system response steady-state value y collected in step S2 s1 and the second system response steady-state value y s2 , calculate the equivalent resistance R0 of the receiving coil: R bn =R b +R n n=1,2 5. The method for parameter identification and real-time calibration of a pulsed eddy current receiving system based on underdamped dynamic response according to claim 4, characterized in that: In step S4, at the known natural frequency ω n1 , damping ratio ζ1, R0, R1 and R b In the case of specific values, according to ω n1 、ζ1 expression: It can be seen that ω n1 , ζ1 is only related to the inductance L and distributed capacitance C of the receiving coil, thereby establishing a mapping relationship between the natural frequency, damping ratio and the inductance L and distributed capacitance C of the receiving coil.

6. The method for parameter identification and real-time calibration of a pulsed eddy current receiving system based on underdamped dynamic response according to claim 5, characterized in that: Step S5 specifically includes the following steps: First, when designing the receiving system, the parameters of the receiving coil are measured and the measured values ​​are set as the initial values ​​of the unknown quantities L and C; Then, the unknowns are updated alternately, and the dual nonlinear equations are expressed as: Fix C and solve for L: In the first iteration, use f1 = (L, C) = 0, f2 = (L, C) = 0, and use Newton's method to solve for the new value of L; Fix L and solve for C: In the next iteration, use f1 = (L, C) = 0, f2 = (L, C) = 0, and use Newton's method to solve for the value of C; Continue to update L and C alternately until the convergence criteria are met; In each alternating update process, the residual change is monitored to determine whether the optimization has converged stably; The error requirement ε is used to limit the number of iterations and adjust the solution accuracy of L and C, thereby realizing the parameter identification of the receiving coil inductance and distributed capacitance.

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