CN118112680A - Calibration method for magnetic ranging probe tube fluxgate sensor - Google Patents
Calibration method for magnetic ranging probe tube fluxgate sensor Download PDFInfo
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- CN118112680A CN118112680A CN202211510877.6A CN202211510877A CN118112680A CN 118112680 A CN118112680 A CN 118112680A CN 202211510877 A CN202211510877 A CN 202211510877A CN 118112680 A CN118112680 A CN 118112680A
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- 230000002068 genetic effect Effects 0.000 claims abstract description 24
- 238000012549 training Methods 0.000 claims description 18
- 238000012360 testing method Methods 0.000 claims description 12
- 210000002445 nipple Anatomy 0.000 abstract description 11
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
- G01V13/00—Manufacturing, calibrating, cleaning, or repairing instruments or devices covered by groups G01V1/00 – G01V11/00
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- E—FIXED CONSTRUCTIONS
- E21—EARTH OR ROCK DRILLING; MINING
- E21B—EARTH OR ROCK DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS
- E21B49/00—Testing the nature of borehole walls; Formation testing; Methods or apparatus for obtaining samples of soil or well fluids, specially adapted to earth drilling or wells
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R33/00—Arrangements or instruments for measuring magnetic variables
- G01R33/0023—Electronic aspects, e.g. circuits for stimulation, evaluation, control; Treating the measured signals; calibration
- G01R33/0035—Calibration of single magnetic sensors, e.g. integrated calibration
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R35/00—Testing or calibrating of apparatus covered by the other groups of this subclass
- G01R35/005—Calibrating; Standards or reference devices, e.g. voltage or resistance standards, "golden" references
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Abstract
The invention relates to the technical field of calibration of a magnetic ranging guide system of a relief well, in particular to a calibration method for a magnetic ranging probe tube fluxgate sensor, which comprises the steps of constructing a calibration environment without a magnetic field or with a low magnetic field; the magnetic field magnitude measured value set is utilized to learn and train a coil calibration model established by a genetic algorithm, so that the triaxial coil calibration of the controllable magnetic field is completed; replacing the calibrated high-precision fluxgate sensor with a magnetic ranging probe to be calibrated; and (3) utilizing the magnetic field strength measurement value set to learn and train the probe calibration model established by utilizing a genetic algorithm, and completing the magnetic distance measurement probe calibration. In order to more accurately measure the stratum low-frequency weak magnetic signal, the invention sets and utilizes the triaxial coil structure for constructing the nonmagnetic calibration environment to construct the environment without magnetic field or the environment with low magnetic field, and realizes the calibration of the exploring tube nipple by twice calibration, thereby eliminating the error of the exploring tube nipple to the greatest extent, accurately measuring the stratum low-frequency weak magnetic signal and realizing the accurate calibration of the exploring tube nipple.
Description
Technical Field
The invention relates to the technical field of calibration of a magnetic ranging guide system of a relief well, in particular to a calibration method for a magnetic ranging probe tube fluxgate sensor.
Background
The triaxial fluxgate sensor is used for a probe nipple in a rescue well magnetic distance measuring and guiding system to measure an alternating magnetic field signal link generated by excitation current converged on an accident well sleeve, so that the relative distance and the relative angle between the rescue well and the accident well are inverted according to magnetic signals. If the relative spatial positions of the rescue well and the accident well are to be accurately inverted, the triaxial sensor is required to accurately measure the weak magnetic signals generated by the sleeve converging current. However, the current three-axis fluxgate sensor is limited by the limitation of processing precision and the characteristics of an electronic circuit, and is easy to cause measurement errors of the three-axis fluxgate sensor of a probe pipe nipple in a magnetic ranging guide system. Therefore, when the measurement is started, the triaxial fluxgate sensor in the probe pipe nipple needs to be calibrated, so that the error of the sensor is eliminated, and the weak magnetic signal measured by the probe pipe nipple in the deep stratum is ensured to be more accurate.
Currently, there are two main methods for calibrating fluxgate sensors: vector and scalar methods. The vector method is to calibrate the three-axis fluxgate sensor by using a known accurate vector magnetic field as a standard, but a plurality of factors need to be considered in an actual experiment, and in addition, the three-axis fluxgate sensor needs to be mounted on a specific carrier for use, so that the influence of errors introduced in the mounting process on the calibration of the three-axis fluxgate sensor is avoided; the scalar method is to adjust error parameters to restore the fitted ellipsoid to a spherical surface, which is also called as an 'ellipsoid fitting method', and the generalization capability of the model is not expanded from the development of a calibrated mathematical model until now.
Disclosure of Invention
The invention provides a calibration method for a magnetic ranging probe tube fluxgate sensor, which overcomes the defects of the prior art, and can effectively solve the problem that the probe tube in the existing calibration method is inaccurate in measuring stratum low-frequency weak magnetic signals.
One of the technical schemes of the invention is realized by the following measures: a calibration method for a magnetic ranging probe fluxgate sensor, comprising a calibration device and a control device, the calibration device comprising a tri-axial coil configured to provide a non-magnetic calibration environment and a tri-axial coil configured to generate a controllable magnetic field, the calibration method comprising:
Constructing a calibration environment without magnetic field or a low magnetic field environment by utilizing a triaxial coil for constructing a non-magnetic calibration environment, placing the triaxial coil for generating a controllable magnetic field in a central area inside the non-magnetic field or the low magnetic field environment, and placing a high-precision fluxgate sensor in the central position of the triaxial coil for generating the controllable magnetic field;
The control device applies current to the triaxial coil of the controllable magnetic field in combination with the set current setting value set, and collects a corresponding magnetic field magnitude measured value set;
The magnetic field magnitude measured value set is utilized to learn and train a coil calibration model established by a genetic algorithm, so that the triaxial coil calibration of the controllable magnetic field is completed;
replacing the calibrated high-precision fluxgate sensor in the triaxial coil generating the controllable magnetic field with a magnetic ranging probe tube to be calibrated, applying current to the triaxial coil generating the controllable magnetic field by the control device in combination with the set current setting value set, and collecting the corresponding magnetic field intensity measuring value set;
And (3) utilizing the magnetic field strength measurement value set to learn and train the probe calibration model established by utilizing a genetic algorithm, and completing the magnetic distance measurement probe calibration.
The following are further optimizations and/or improvements to the above-described inventive solution:
The control device applies current to the triaxial coil of the controllable magnetic field in combination with the set current setting value set, and collects the corresponding magnetic field magnitude measured value set, and the control device comprises:
setting a current setting value set in the control device, wherein the current setting value set comprises a plurality of current values applied to the triaxial coils of the controllable magnetic field, and step sizes between adjacent current values are the same;
The control device applies current to the triaxial coil of the controllable magnetic field according to the current set value set, and collects magnetic field magnitude measured values measured by the high-precision fluxgate sensor to form a magnetic field magnitude measured value set.
The control device applies current to the triaxial coil of the controllable magnetic field in combination with the set current set value set, and collects a corresponding magnetic field strength measured value set, and the control device comprises:
setting a current setting value set in the control device, wherein the current setting value set comprises a plurality of current values applied to the triaxial coils of the controllable magnetic field, and step sizes between adjacent current values are the same;
The control device applies current to the triaxial coil of the controllable magnetic field according to the current set value set, and collects magnetic field intensity measured values detected by the magnetic distance measuring probe tube to form a magnetic field intensity measured value set.
The above-mentioned utilize magnetic field magnitude measured value set to utilize genetic algorithm to establish the coil calibration model and learn the training, accomplish the triaxial coil calibration of controllable magnetic field and utilize magnetic field intensity measured value set to utilize genetic algorithm to establish the process of detecting tube calibration model and learn the training the same, accomplish the process of magnetic range finding detecting tube calibration, wherein utilize magnetic field magnitude measured value set to utilize genetic algorithm to establish the triaxial coil calibration model and learn the training, accomplish the triaxial coil calibration of controllable magnetic field, include:
dividing the magnetic field magnitude measurement set into a modeling data set and a test data set according to a ratio of 8:2;
learning and training a coil calibration model established by using a genetic algorithm by using a modeling data set to obtain a model coefficient optimal solution of the coil calibration model;
And verifying a coil calibration model brought into the optimal solution of the model coefficient by using the test data set, determining whether the error is in a set range, and if so, reserving the model coefficient to finish the triaxial coil calibration of the controllable magnetic field.
The control device comprises a current control module, a data acquisition module and a main control module;
the current control module is used for applying current to the triaxial coil without the magnetic calibration environment and the triaxial coil generating the controllable magnetic field;
The data acquisition module is used for acquiring measured values detected by the high-precision fluxgate sensor and the magnetic ranging probe;
and the main control module is used for controlling the current control module and the data acquisition module and executing the calibration method.
The triaxial coil for constructing the non-magnetic calibration environment and the triaxial coil for generating the controllable magnetic field are Helmholtz coils with mutually perpendicular triaxial.
In order to more accurately measure the stratum low-frequency weak magnetic signal by the high-precision fluxgate sensor and the magnetic distance measuring probe, the magnetic distance measuring probe calibration is accurately implemented, and the calibration is required to be carried out in a zero magnetic field environment or a zero magnetic field environment as far as possible, so that the invention sets and utilizes the triaxial coil structure for constructing the non-magnetic calibration environment to construct the non-magnetic field or the low-magnetic field environment, and realizes the calibration of the probe nipple by twice calibration (the calibration of the triaxial coil of the controllable magnetic field and the calibration of the magnetic distance measuring probe), thereby eliminating the self error as much as possible, accurately measuring the stratum low-frequency weak magnetic signal and realizing the accurate calibration of the probe nipple.
Drawings
Fig. 1 is a schematic diagram of the circuit connection of the present invention.
FIG. 2 is a flow chart of the calibration method of the present invention.
FIG. 3 is a flow chart of a method of constructing a calibrated environment free of magnetic fields in the present invention.
FIG. 4 is a flow chart of a method for calibrating coils in the invention.
FIG. 5 is a flow chart of a method for calibrating a magnetic ranging probe according to the present invention.
Detailed Description
The present invention is not limited by the following examples, and specific embodiments can be determined according to the technical scheme and practical situations of the present invention.
The invention is further described below with reference to examples and figures:
Example 1: as shown in fig. 1 and 2, an embodiment of the present invention discloses a calibration method for a magnetic ranging probe fluxgate sensor, which is characterized by comprising a calibration device and a control device, wherein the calibration device comprises a triaxial coil for constructing a non-magnetic calibration environment and a triaxial coil for generating a controllable magnetic field, and the calibration method comprises:
S101, constructing a calibration environment non-magnetic field or low magnetic field environment by utilizing a triaxial coil for constructing a non-magnetic calibration environment, placing the triaxial coil for generating a controllable magnetic field in a central area inside the non-magnetic field or low magnetic field environment, and placing a high-precision fluxgate sensor in the central position of the triaxial coil for generating the controllable magnetic field;
step S102, a control device applies current to a triaxial coil of a controllable magnetic field in combination with a set current setting value set, and a corresponding magnetic field magnitude measurement value set is acquired;
Step S103, learning and training a coil calibration model established by a genetic algorithm by utilizing a magnetic field magnitude measurement value set to finish the triaxial coil calibration of the controllable magnetic field;
step S104, replacing the calibrated high-precision fluxgate sensor in the triaxial coil for generating the controllable magnetic field with a magnetic ranging probe to be calibrated, applying current to the triaxial coil of the controllable magnetic field by the control device in combination with the set current setting value set, and collecting the corresponding magnetic field intensity measuring value set;
And step S105, learning and training the probe calibration model established by the genetic algorithm by utilizing the magnetic field strength measurement value set to finish magnetic ranging probe calibration.
In order to more accurately measure the stratum low-frequency weak magnetic signal by the high-precision fluxgate sensor and the magnetic distance measuring probe, the magnetic distance measuring probe calibration is accurately implemented, and the calibration is required to be carried out in a zero magnetic field environment or a zero magnetic field environment as far as possible, so that the invention sets and utilizes the triaxial coil structure for constructing the non-magnetic calibration environment to construct the non-magnetic field or the low-magnetic field environment, and realizes the calibration of the probe nipple by twice calibration (the calibration of the triaxial coil of the controllable magnetic field and the calibration of the magnetic distance measuring probe), thereby eliminating the self error as much as possible, accurately measuring the stratum low-frequency weak magnetic signal and realizing the accurate calibration of the probe nipple.
In the above steps, steps S102 to S103 achieve the calibration of the triaxial coil of the controllable magnetic field, and steps S104 to S105 achieve the calibration of the magnetic ranging probe.
The calibration device comprises a triaxial coil for constructing a non-magnetic calibration environment and a triaxial coil for generating a controllable magnetic field, wherein the triaxial coil for constructing the non-magnetic calibration environment and the triaxial coil for generating the controllable magnetic field can be Helmholtz coils with three mutually perpendicular axes. The three-axis coil generating the controllable magnetic field is dimensioned as much as 2 times the maximum dimension of the magnetic ranging probe to be calibrated, but at the same time fulfils half the minimum dimension of the three-axis helmholtz coil for constructing a zero magnetic field environment.
The error of a triaxial coil that produces a controllable magnetic field consists mainly of three parts: the three-axis coil calibration formula of the controllable magnetic field based on the existing errors is as follows:
Where i is the row vector [ Ix, iy, iz ] T, i T is the transpose of i, the row vectors k, u, y and the diagonal matrix D Q are in the form:
example 2: as shown in fig. 3, an embodiment of the present invention discloses a calibration method for a magnetic ranging probe fluxgate sensor, wherein a calibration environment is a no-magnetic field or low-magnetic field environment is constructed by using a triaxial coil for constructing a no-magnetic calibration environment, comprising:
step S201, the control device applies current to the triaxial coil for constructing the non-magnetic field environment;
In step S202, the control device adjusts the magnitude of the applied current so that the uniform magnetic field generated inside the triaxial coil configured to have no magnetic field environment counteracts the magnetic field around the calibration environment, and configures the calibration environment to have no magnetic field or a low magnetic field environment.
Example 3: as shown in fig. 4, the embodiment of the invention discloses a calibration method for a magnetic ranging probe tube fluxgate sensor, wherein the process of calibrating a triaxial coil of a controllable magnetic field comprises the following steps:
step S301, a triaxial coil generating a controllable magnetic field is placed in a central area in a non-magnetic field or low-magnetic field environment, and a high-precision fluxgate sensor is placed in the central position of the triaxial coil generating the controllable magnetic field;
Step S302, a current setting value set is set in a control device, wherein the current setting value set comprises a plurality of current values applied to a triaxial coil of a controllable magnetic field, and step sizes between adjacent current values are the same;
Step S303, the control device applies current to the triaxial coil of the controllable magnetic field according to the current set value set, and collects magnetic field magnitude measured values measured by the high-precision fluxgate sensor to form a magnetic field magnitude measured value set; the data amount of the magnetic field magnitude measurement value is not less than 100 groups;
Step S304, learning and training a coil calibration model established by a genetic algorithm by utilizing a magnetic field magnitude measurement value set, and completing the triaxial coil calibration of the controllable magnetic field, wherein the method comprises the following steps:
(1) Dividing the magnetic field magnitude measurement set into a modeling data set and a test data set according to a ratio of 8:2;
(2) Learning and training a coil calibration model established by using a genetic algorithm by using a modeling data set to obtain a model coefficient optimal solution of the coil calibration model;
(3) And verifying a coil calibration model brought into the optimal solution of the model coefficient by using the test data set, determining whether the error is within a set range (namely, whether the deviation average value of the test data set is within the set range), if so, reserving the model coefficient, finishing the calibration of the triaxial coil of the controllable magnetic field, and if not, returning to the step S302.
Example 4: as shown in fig. 5, an embodiment of the invention discloses a calibration method for a magnetic ranging probe fluxgate sensor, wherein the process of calibrating the magnetic ranging probe comprises the following steps:
step S401, replacing a calibrated high-precision fluxgate sensor in a triaxial coil for generating a controllable magnetic field with a magnetic ranging probe to be calibrated;
step S402, a current setting value set is set in a control device, wherein the current setting value set comprises a plurality of current values applied to a triaxial coil of a controllable magnetic field, and step sizes between adjacent current values are the same;
step S403, the control device applies current to the triaxial coil of the controllable magnetic field according to the current set value set, and collects magnetic field intensity measured values detected by the magnetic ranging probe tube to form a magnetic field intensity measured value set;
Step S404, learning and training the probe calibration model established by the genetic algorithm by utilizing the magnetic field strength measurement value set to complete the magnetic ranging probe calibration, comprising the following steps:
(1) Dividing the magnetic field strength measurement value set into a modeling data set and a test data set according to a ratio of 8:2;
(2) Learning and training a coil calibration model established by using a genetic algorithm by using a modeling data set to obtain a model coefficient optimal solution of the coil calibration model;
(3) And verifying a probe calibration model brought into the optimal solution of the model coefficient by using the test data set, determining whether the error is within a set range (namely whether the deviation average value of the test data set is within the set range), if so, reserving the model coefficient, finishing the magnetic ranging probe calibration, and if not, returning to the step S402.
Example 5: as shown in fig. 1, the embodiment of the invention discloses a calibration method for a magnetic ranging probe tube fluxgate sensor, wherein a control device comprises a current control module, a data acquisition module and a main control module;
The current control module is used for applying current to the triaxial coil without the magnetic calibration environment and the triaxial coil generating the controllable magnetic field; the current control module can be a programmable high-precision direct current power supply produced by aviation companies: HY-PPM.
The data acquisition module is used for acquiring measured values detected by the high-precision fluxgate sensor and the magnetic ranging probe;
And the main control module is used for controlling the current control module and the data acquisition module and executing the calibration method. The main control module can be an upper computer.
The technical characteristics form the optimal embodiment of the invention, have stronger adaptability and optimal implementation effect, and can increase or decrease unnecessary technical characteristics according to actual needs so as to meet the requirements of different situations.
Claims (9)
1. A calibration method for a magnetic ranging probe fluxgate sensor, comprising a calibration device and a control device, wherein the calibration device comprises a triaxial coil for constructing a non-magnetic calibration environment and a triaxial coil for generating a controllable magnetic field, the calibration method comprising:
Constructing a calibration environment without magnetic field or a low magnetic field environment by utilizing a triaxial coil for constructing a non-magnetic calibration environment, placing the triaxial coil for generating a controllable magnetic field in a central area inside the non-magnetic field or the low magnetic field environment, and placing a high-precision fluxgate sensor in the central position of the triaxial coil for generating the controllable magnetic field;
The control device applies current to the triaxial coil of the controllable magnetic field in combination with the set current setting value set, and collects a corresponding magnetic field magnitude measured value set;
The magnetic field magnitude measured value set is utilized to learn and train a coil calibration model established by a genetic algorithm, so that the triaxial coil calibration of the controllable magnetic field is completed;
replacing the calibrated high-precision fluxgate sensor in the triaxial coil generating the controllable magnetic field with a magnetic ranging probe tube to be calibrated, applying current to the triaxial coil generating the controllable magnetic field by the control device in combination with the set current setting value set, and collecting the corresponding magnetic field intensity measuring value set;
And (3) utilizing the magnetic field strength measurement value set to learn and train the probe calibration model established by utilizing a genetic algorithm, and completing the magnetic distance measurement probe calibration.
2. The method for calibrating a magnetic ranging probe fluxgate sensor according to claim 1, wherein the controlling means applies a current to the tri-axial coil of the controllable magnetic field in combination with the set of set current setting values, and collects a corresponding set of magnetic field magnitude measurement values, comprising:
setting a current setting value set in the control device, wherein the current setting value set comprises a plurality of current values applied to the triaxial coils of the controllable magnetic field, and step sizes between adjacent current values are the same;
The control device applies current to the triaxial coil of the controllable magnetic field according to the current set value set, and collects magnetic field magnitude measured values measured by the high-precision fluxgate sensor to form a magnetic field magnitude measured value set.
3. The calibration method for a magnetic ranging probe fluxgate sensor according to claim 1 or 2, wherein the control device applies current to the tri-axial coils of the controllable magnetic field in combination with the set current set value set, and collects the corresponding set of magnetic field strength measurement values, comprising:
setting a current setting value set in the control device, wherein the current setting value set comprises a plurality of current values applied to the triaxial coils of the controllable magnetic field, and step sizes between adjacent current values are the same;
The control device applies current to the triaxial coil of the controllable magnetic field according to the current set value set, and collects magnetic field intensity measured values detected by the magnetic distance measuring probe tube to form a magnetic field intensity measured value set.
4. The calibration method for a magnetic ranging probe fluxgate sensor according to claim 1 or 2, wherein the learning training of the coil calibration model established by the genetic algorithm by using the magnetic field magnitude measurement value set, the three-axis coil calibration of the controllable magnetic field, and the learning training of the probe calibration model established by the genetic algorithm by using the magnetic field strength measurement value set are completed, and the process of completing the calibration of the magnetic ranging probe is the same, wherein the learning training of the coil calibration model established by the genetic algorithm by using the magnetic field magnitude measurement value set, and the three-axis coil calibration of the controllable magnetic field are completed, and the method comprises:
dividing the magnetic field magnitude measurement set into a modeling data set and a test data set according to a ratio of 8:2;
learning and training a coil calibration model established by using a genetic algorithm by using a modeling data set to obtain a model coefficient optimal solution of the coil calibration model;
And verifying a coil calibration model brought into the optimal solution of the model coefficient by using the test data set, determining whether the error is in a set range, and if so, reserving the model coefficient to finish the triaxial coil calibration of the controllable magnetic field.
5. The calibration method for a magnetic ranging probe fluxgate sensor according to claim 3, wherein the learning training of the coil calibration model established by the genetic algorithm using the magnetic field magnitude measurement value set, the three-axis coil calibration of the controllable magnetic field being completed, and the learning training of the probe calibration model established by the genetic algorithm using the magnetic field strength measurement value set, the same process of completing the magnetic ranging probe calibration, wherein the learning training of the coil calibration model established by the genetic algorithm using the magnetic field magnitude measurement value set, the three-axis coil calibration of the controllable magnetic field being completed, comprises:
dividing the magnetic field magnitude measurement set into a modeling data set and a test data set according to a ratio of 8:2;
learning and training a coil calibration model established by using a genetic algorithm by using a modeling data set to obtain a model coefficient optimal solution of the coil calibration model;
And verifying a coil calibration model brought into the optimal solution of the model coefficient by using the test data set, determining whether the error is in a set range, and if so, reserving the model coefficient to finish the triaxial coil calibration of the controllable magnetic field.
6. The calibration method for the magnetic ranging probe fluxgate sensor according to claim 1, 2 or 5, wherein the control device comprises a current control module, a data acquisition module and a main control module;
the current control module is used for applying current to the triaxial coil without the magnetic calibration environment and the triaxial coil generating the controllable magnetic field;
The data acquisition module is used for acquiring measured values detected by the high-precision fluxgate sensor and the magnetic ranging probe;
and the main control module is used for controlling the current control module and the data acquisition module and executing the calibration method.
7. The calibration method for the magnetic ranging probe fluxgate sensor according to claim 3 or 4, wherein the control device comprises a current control module, a data acquisition module and a main control module;
the current control module is used for applying current to the triaxial coil without the magnetic calibration environment and the triaxial coil generating the controllable magnetic field;
The data acquisition module is used for acquiring measured values detected by the high-precision fluxgate sensor and the magnetic ranging probe;
and the main control module is used for controlling the current control module and the data acquisition module and executing the calibration method.
8. The calibration method for a magnetic ranging probe fluxgate sensor according to any one of claims 1 to 7, wherein the calibrating environment is a no-magnetic field or low-magnetic field environment using a tri-axial coil configuration of a no-magnetic calibration environment, comprising:
the control device applies current to the triaxial coil which is constructed in a non-magnetic field environment;
The control device adjusts the magnitude of the applied current so that a uniform magnetic field generated inside the triaxial coil for constructing the non-magnetic field environment counteracts the magnetic field around the calibration environment, and constructs the non-magnetic field or low-magnetic field environment of the calibration environment.
9. The calibration method for a magnetic ranging probe fluxgate sensor according to any one of claims 1 to 8, wherein the triaxial coil constructing the non-magnetic calibration environment and the triaxial coil generating the controllable magnetic field are helmholtz coils having three axes perpendicular to each other.
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