CN115453635A - Fractional order induction-magnetization equivalent ring device and design method - Google Patents
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Abstract
The invention relates to a fractional order induction-magnetization equivalent ring device and a design method thereof, wherein the induction-magnetization equivalent ring device is formed by connecting an induction coil and a plurality of RL circuits in parallel, wherein the induction coil is used for generating mutual inductance with a transmitting coil so as to generate induced current on each branch circuit, eddy currents generated by each RL branch circuit are not interfered with each other, induced electromotive force finally generated by the induction-magnetization equivalent ring is the sum of induced voltages generated after each branch circuit is switched off, and the inductance and the resistance value of each branch circuit of equivalent target induction-magnetization response are determined by utilizing a chaotic quantum particle swarm algorithm and a least square fitting method, so that equivalent approximation of induction-magnetization effect of any fractional order in a target time period is realized. The invention aims to perform equivalent approximation on the induction-magnetization effect so as to analyze the attenuation rule and the characteristics of the induction-magnetization effect and influence on the field practical application process of the time domain electromagnetic method, thereby improving the detection precision of the time domain electromagnetic method in the magnetic environment.
Description
Technical Field
The invention relates to a fractional order induction-magnetization equivalent ring device and a design method in the field of geophysical exploration.
Background
The induction-magnetization effect is a slow decay phenomenon produced by ferromagnetic particles. In particular, the super paramagnetic effect generated by the shallow ferromagnetic particles and the viscous remanence effect generated by the deep ferromagnetic minerals are shown. In the detection process of the transient electromagnetic method, the on-time stage of the emission current can change the direction of underground magnetic particles to obtain magnetization; after the current is switched off, the magnetic particles lose their magnetization and the receiving system observes a decaying signal at approximately-1 power. The experimental results at home and abroad show that the induction-magnetization effect not only shows the-1 power law attenuation in the middle and late stages of the attenuation curve, but also shows the fractional order attenuation law when the attenuation curve is in the range of-1 +/-0.4 more times. Meanwhile, the induction-magnetization effect not only can interfere the data interpretation, but also can be identified as the characteristic of a ferromagnetic mineral. How to eliminate the interference of the induction-magnetization effect or utilize the interference to accurately position ferromagnetic minerals becomes a problem which needs to be solved urgently by researchers.
CN102096113A discloses a time domain ground-air electromagnetic detection system and calibration method, which uses an abnormal loop sensing signal recording device composed of a resistor and an inductor to realize the test and calibration of the detection system, and becomes a method for test and analysis in the field of geophysical, but only can characterize a simple eddy current effect, and has great limitations.
CN113504571A discloses a polarization equivalent ring device of a multiphase conductive medium and a design method thereof, which adopts a polarization ring device composed of a capacitor and a resistor, thereby realizing characterization of an induction-polarization effect of the multiphase conductive medium, and greatly facilitating analysis and detection of the induction-polarization effect.
CN113887106A discloses a method for simulating induction-magnetization effect three-dimensional numerical values based on a Chikazumi model, which performs three-dimensional numerical simulation on induction-magnetization effect of integer order, and is beneficial to representing attenuation law of induction-magnetization effect.
CN113779853A discloses a time domain electromagnetic induction-magnetization effect fractional order three-dimensional numerical simulation method, which utilizes a Cole-Cole susceptibility model to carry out three-dimensional numerical simulation on fractional order induction-magnetization effect, and is closer to the induction-magnetization effect in the actual detection process.
Currently, most of research on the induction-magnetization effect focuses on forward and backward numerical simulation calculation, and how to perform targeted detection on the induction-magnetization effect needs to combine numerical simulation and actual detection by using the idea of an abnormal ring, so as to realize targeted measurement and observation on the induction-magnetization effect.
Disclosure of Invention
The invention aims to utilize the abnormal ring theory for popularization and establishment, a plurality of RL parallel induction-magnetization equivalent circuits are established, and a fractional order induction-magnetization equivalent ring device in a target time period and a design method are provided by utilizing the characteristics that the RL circuits after parallel connection are not interfered with each other and the generated induced electromotive forces are mutually superposed.
The present invention is achieved by a fractional order induction-magnetization equivalent ring device, comprising:
the induction-magnetization equivalent loop circuit is formed by connecting a plurality of RL circuits, a coil and a resistor in parallel, wherein each group of RL circuits are in parallel relation and are different from a conventional abnormal loop circuit or a conventional polarized loop circuit; each RL branch consists of a resistor and an inductor which are connected in series, and the number of the RL branches is related to the equivalent induction-magnetization effect of a target; the coil is wound by a thin wire, the inductance of the coil is far smaller than that of the branches, and the coil is used for receiving the excitation of an external magnetic field, so that induced current is generated in each branch; the induced electromotive force after the superposition of each branch can be in slope attenuation within the range of minus 1 +/-0.4 between the middle and late stages of the attenuation curve, so that the induction-magnetization effect is equivalently represented. The method can be used for experimental observation and calibration of the induction-magnetization effect, plays a role in assisting in processing and analyzing induction-magnetization effect data, and provides theoretical guidance for instrument design aiming at the induction-magnetization effect.
A method of designing a fractional order induction-magnetization equivalent ring device, the method comprising:
1) By making measurements, the inductance L of the coil is determined 0 And the total resistance R of the branch in which the resistor is positioned 0 The size of the magnetic field is determined, and the starting time of the decay slope and the slow decay of the induction-magnetization response which need to be equivalent is determined through numerical simulation;
2) Setting the number of the RL branch circuit groups connected in parallel as N, and calculating an induced electromotive force expression generated in an induction-magnetization equivalent circuit under the excitation of a ramp step waveform by utilizing mutual inductance calculation among coils and an equivalent circuit theory;
3) Setting the value range of each branch inductance and resistance according to the actual device standard by using a chaotic quantum particle swarm algorithm, and calculating the inductance value L of each branch with the induced electromotive force attenuation slope closest to the target slope in the target time period according to the least square fitting theory 1 ，L 2 ，L 3 ，…，L N And resistance value R 1 ，R 2 ，R 3 ，…，R N ；
4) By changing the inductance value and the resistance value of each branch and the number of the branches, the parameter result of each branch of the induction-magnetization equivalent ring with any fractional order within a short target time can be approximated;
5) The inductors of all the branches are connected in series with the resistors and then connected in parallel with the coils to form an induction-magnetization equivalent ring, and a time-varying electromagnetic field is applied to the induction-magnetization equivalent ring, so that the induction-magnetization effect can be equivalently approximated, and the analysis and calibration of the characteristics of the induction-magnetization effect in a time domain electromagnetic method are facilitated;
further, in the step 2), because the RL branches are not affected by each other and the generated magnetic fields are mutually superposed, the RL branches can be equivalent to a plurality of eddy current effects which are attenuated by e exponential, and RL parameters can be allocated, so that the total response can be attenuated by any fractional order with the slope of-1 ± 0.4 at the middle and late stages, and the induced electromotive force expression of the induction-magnetization equivalent ring under the excitation of the ramp step waveform is as follows:
wherein M is TL Is the mutual inductance between the transmitter coil and the anomalous coil, M RL Is the mutual inductance between the receiver coil and the abnormal coil, I is the amplitude of the transmitted current, T 1 For current rise time, T 2 For current fall time, T 3 For the emission current width, the time constant of each branch is
Further, in the step 3), the chaotic quantum particle swarm algorithm is used for selecting parameters of each branch, and meanwhile, the least square fitting theory is adopted for judging the fitting result,
wherein, f (x) 1 ,x 2 ,…,x N )＝{log[V(n+1)]-log[V(n)]}/{log[t(n+1)]-log[t(n)]}，y i ＝log(t m )(m＝-1±0.4)。
Compared with the prior art, the invention has the beneficial effects that:
the fractional order induction-magnetization equivalent ring device provided by the invention utilizes the eddy current effect of the abnormal ring to perform equivalent approximation on the attenuation characteristics of the induction-magnetization effect of any fractional order in a target time period in the middle and late stages, analyzes and simulates the induction-magnetization effect in a circuit form, can be excited by the transmitting coil, receives the induced electromotive force generated by the induction-magnetization equivalent ring by the receiving coil, analyzes and verifies the law of the induction-magnetization effect, effectively combines numerical simulation and experimental verification, simultaneously reduces the experimental difficulty of the induction-magnetization effect, and provides guidance for the design of corresponding instruments.
Drawings
FIG. 1 is a flow chart of a design of a fractional order induction-magnetization equivalent ring device;
FIG. 2 is a block diagram of a fractional order induction-magnetization equivalent ring arrangement;
FIG. 3 is a graph showing a response calculation of induced electromotive force of a fractional induction-magnetization equivalent ring;
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to the following embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
According to the invention, a fractional order induction-magnetization equivalent ring device is designed according to an abnormal ring equivalent circuit model and a fractional order Cole-Cole magnetic susceptibility model theory, a plurality of RL circuits are connected with coils in parallel, the eddy current effects of all branches are not interfered with each other and are mutually overlapped, parameters of all RL branches which can approach a target slope are solved through a chaotic quantum particle swarm algorithm and a least square fitting method, the induced electromotive force of an abnormal coil is calculated and compared with the target slope, the accuracy of the device is verified, and a flow chart is shown in figure 1.
The present invention is achieved in that, as shown in fig. 2, a fractional order induction-magnetization equivalent ring apparatus includes:
the circuit of the induction-magnetization equivalent ring is formed by connecting a plurality of RL circuits with a coil and a resistor in parallel; each RL branch consists of a resistor and an inductor which are connected in series, and the number of the RL branches is related to the equivalent induction-magnetization response of a target; the coil is wound by a thin wire, the inductance of the coil is far smaller than that of the branches, and the coil is used for receiving the excitation of an external magnetic field, so that induced current is generated in each branch.
A method of designing a fractional order induction-magnetization equivalent ring device, the method comprising:
1) By making measurements, the inductance L of the coil is determined 0 And the total resistance R of the branch in which the resistor is positioned 0 The size of the magnetic field is determined, and the starting time of the decay slope and the slow decay of the induction-magnetization response which need to be equivalent is determined through numerical simulation;
2) Because the RL branches do not influence each other and the generated magnetic fields are mutually superposed, the RL branches can be equivalent to a plurality of eddy current effects with e exponential attenuation, and the total response can be attenuated in any fractional order with the slope of minus 1 +/-0.4 at the middle and later stages by allocating RL parameters; the number of sets of RL branches connected in parallel is set to be N, and an induced electromotive force expression generated in an induction-magnetization equivalent circuit under the excitation of a ramp step waveform is calculated by utilizing mutual inductance calculation among coils and an equivalent circuit theory as follows:
wherein M is TL Is the mutual inductance between the transmitter coil and the anomalous coil, M RL Is the mutual inductance between the receiver coil and the abnormal coil, I is the amplitude of the transmitted current, T 1 As current rise time, T 2 For current fall time, T 3 For emission current width, the time constant of each branch is
3) Setting the value range of each branch inductance and resistance according to the actual device standard by using a chaotic quantum particle swarm algorithm, judging a fitting result according to a least square fitting theory, and calculating the inductance value L of each branch with the induced electromotive force attenuation slope closest to a target slope in a target time period 1 ，L 2 ，L 3 ，…，L N And a resistance value R 1 ，R 2 ，R 3 ，…，R N ；
Wherein, f (x) 1 ,x 2 ,…,x N )＝{log[V(n+1)]-log[V(n)]}/{log[t(n+1)]-log[t(n)]}，y i ＝log(t m )(m＝-1±0.4)。
4) By changing the inductance value and the resistance value of each branch and the number of the branches, the parameter result of each branch of the induction-magnetization equivalent ring with any fractional order within the target time can be approximated;
5) The inductors of all the branches are connected in series with the resistors and then connected in parallel with the coils to form an induction-magnetization equivalent ring, and a time-varying electromagnetic field is applied to the induction-magnetization equivalent ring, so that the induction-magnetization effect can be equivalently approximated, and the analysis and calibration of the characteristics of the induction-magnetization effect in a time domain electromagnetic method are facilitated;
verification of the induced electromotive force response of the induction-magnetization equivalent ring is shown in fig. 3.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents and improvements made within the spirit and principle of the present invention are intended to be included within the scope of the present invention.
Claims (4)
1. A fractional order induction-magnetization equivalent ring device is characterized in that the device is formed by connecting a plurality of RL circuits with a coil and a resistor in parallel, wherein each group of RL circuits are in parallel relation and are different from a conventional abnormal ring circuit or a conventional polarized ring circuit; each RL branch consists of a resistor and an inductor which are connected in series, and the number of the RL branches is related to the equivalent induction-magnetization response of a target; the coil is wound by a thin wire, the inductance of the coil is far smaller than that of the branches, and the coil is used for receiving the excitation of an external magnetic field, so that induced current is generated in each branch.
2. A method of designing a fractional order induction-magnetization equivalent ring device according to claim 1, comprising:
1) By making measurements, the inductance L of the coil is determined 0 And the total resistance R of the branch in which the resistor is positioned 0 The size of the magnetic field is determined, and the starting time of the decay slope and the slow decay of the induction-magnetization response which need to be equivalent is determined through numerical simulation;
2) The number of sets of RL branches connected in parallel is set to be N, and an induced electromotive force expression generated in an induction-magnetization equivalent circuit under the excitation of a ramp step waveform is calculated by utilizing mutual inductance calculation among coils and an equivalent circuit theory;
3) Setting the value range of each branch inductance and resistance according to the actual device standard by using a chaotic quantum particle swarm algorithm, and calculating the inductance value L of each branch with the induced electromotive force attenuation slope closest to the target slope in the target time period according to the least square fitting theory 1 ，L 2 ，L 3 ，...，L N And resistance value R 1 ，R 2 ，R 3 ，...，R N ；
4) By changing the inductance value and the resistance value of each branch and the number of the branches, the parameter result of each branch of the induction-magnetization equivalent ring with any fractional order within a short target time can be approximated;
5) Each branch inductor is connected in series with a resistor and then connected in parallel with a coil to form an induction-magnetization equivalent ring, and a time-varying electromagnetic field is applied to the induction-magnetization equivalent ring, so that the induction-magnetization effect can be equivalently approximated, and the analysis and calibration of the characteristics of the induction-magnetization effect in the time domain electromagnetic method are facilitated.
3. The method according to claim 2, wherein in step 2), because the RL branches do not affect each other and the generated magnetic fields are mutually superposed, the RL branches can be equivalent to a plurality of eddy current effects with e exponential decay, the RL parameters can be adjusted, so that the total response presents any fractional order decay with the slope of-1 ± 0.4 in the middle and late stages, and the induced electromotive force expression of the induction-magnetization equivalent loop under the excitation of the ramp waveform is as follows:
wherein, M TL Is the mutual inductance between the transmitter coil and the anomalous coil, M RL Is the mutual inductance between the receiver coil and the abnormal coil, I is the amplitude of the transmitted current, T 1 As current rise time, T 2 For current fall time, T 3 For emission current width, the time constant of each branch is
4. The method according to claim 2, wherein in step 3), the parameters of each branch are selected by using a chaotic quantum particle swarm algorithm, and the fitting result is judged by using a least square fitting theory,
wherein, f (x) 1 ,x 2 ,…,x N )＝{log[V(n+1)]-log[V(n)]}/{log[t(n+1)]-log[t(n)]}，y i ＝log(t m )(m＝-1±0.4)。
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