Borehole three-dimensional center line trajectory reconstruction method and measuring probe

Abstract

The application provides a blast hole three-dimensional center line track reconstruction method and a measuring probe. A mechanical structure is used to constrain the axial direction of the measuring probe to be consistent with the local axial direction of the blast hole. An inertial measurement unit is used to obtain the change information of the probe attitude along the arc length direction of the blast hole. An attitude evolution model is constructed with the blast hole arc length as the independent variable to avoid the integral error in the time domain. A physical prior constraint of the blast hole curvature continuity is introduced to self-correct the inertial measurement result. The corrected directional field is spatially integrated to generate the three-dimensional center line track of the blast hole. Thus, the three-dimensional track of the underground blast hole is accurately reconstructed without external reference.

Description

Technical Field

[0001] This application relates to the field of data processing technology, and in particular to a method for reconstructing the three-dimensional centerline trajectory of a borehole and a measuring probe. Background Technology

[0002] In underground metal mine blasting operations, the actual spatial trajectory of the borehole has a significant impact on blasting effectiveness, ore body control, and safe production. However, existing borehole trajectory measurement technologies generally suffer from the following problems:

[0003] 1. Relies on the Global Navigation Satellite System (GPS) or external positioning references, making it unusable in underground environments;

[0004] 2. Relying on a magnetometer for course correction, it is susceptible to magnetic interference from underground metal environments, which can cause it to malfunction.

[0005] 3. Visual or laser scanning methods require identifiable features on the borehole wall, making them unsuitable for borehole environments with smooth walls and highly degraded features;

[0006] 4. Traditional inertial navigation methods obtain position through time-domain integration, but errors accumulate rapidly over time, making it difficult to obtain reliable trajectory results.

[0007] Therefore, there is an urgent need for a technical solution that does not rely on external positioning references, magnetic field information, or borehole wall geometric features, and can stably output the three-dimensional centerline trajectory of the borehole. Summary of the Invention

[0008] This application proposes a method for reconstructing the three-dimensional centerline trajectory of a borehole and a measurement probe, which can solve one of the problems existing in the background art.

[0009] To achieve the above objectives, this application adopts the following technical solution:

[0010] Firstly, a method for reconstructing the three-dimensional centerline trajectory of a borehole is provided. This method is based on a measuring probe. When the measuring probe travels within the borehole, its axial direction is always aligned with the local axis of the borehole. The measuring probe includes an inertial measurement module and an arc length measurement module. The method for reconstructing the three-dimensional centerline trajectory of a borehole includes:

[0011] Obtain inertial data, which reflects the attitude of the measuring probe, measured by the inertial measurement module, and the forward arc length of the measuring probe along the axial direction, measured by the arc length measurement module.

[0012] Based on the constructed attitude evolution model that reflects the change of the attitude of the measuring probe with the forward arc length, the attitude recursion result is obtained;

[0013] Based on the attitude recursion result, the borehole direction vector is obtained;

[0014] Furthermore, the trajectory of the three-dimensional centerline of the borehole is recursively obtained by using the forward arc length, the borehole direction vector, and the initial position of the three-dimensional centerline of the borehole at the forward arc length.

[0015] Based on the above technical solution, mechanical structure constraints are used to ensure that the axis of the measuring probe is always aligned with the local axis of the borehole. Based on the inertial measurement unit, the change information of the probe attitude along the borehole arc length is obtained. An attitude evolution model is constructed with the borehole arc length as the independent variable to avoid time-domain integration errors. A physical prior constraint on the continuity of borehole curvature is introduced to self-correct the inertial measurement results. The corrected orientation field is spatially integrated to generate the three-dimensional centerline trajectory of the borehole. In this way, the accurate reconstruction of the three-dimensional trajectory of the underground borehole is achieved without external reference.

[0016] In one possible design of the first aspect, the probe coordinate system {B} of the measuring probe and the trajectory reconstruction coordinate system {W} of the three-dimensional centerline trajectory of the borehole are connected by a rotation matrix R. k Transformation, where k is the sampling step.

[0017] In one possible design approach of the first aspect, the inertial data includes angular velocity data, and the attitude evolution model uses the attitude recursion formula as follows:

[0018] Where, ω x,k ,ω y,k ,ω z,k These are the angular velocity components of the X, Y, and Z axes around the probe coordinate system {B}; The antisymmetric matrix of angular velocity; Δs k R is the increment of the forward arc length; k R is the rotation matrix from the probe coordinate system {B} to the trajectory reconstruction coordinate system {W} at step k; k+1 For step k+1, the rotation matrix from the probe coordinate system {B} to the trajectory reconstruction coordinate system {W} is given.

[0019] In one possible design approach for the first aspect, the arc length position s k The borehole direction vector d at the location k for:

[0020] Among them, R k For step k, the rotation matrix from the probe coordinate system {B} to the trajectory reconstruction coordinate system {W}.

[0021] In one possible design of the first aspect, the position of the three-dimensional centerline of the borehole at the advance arc length is obtained recursively in the following manner:

[0022] Where, p k At step k, the three-dimensional centerline of the borehole is at the advancing arc length s k The location of the p; k+1 At step k+1, the three-dimensional centerline of the borehole is at the advancing arc length s k+1 The location of the place; d k Position s of arc length k The borehole direction vector at the location; Δs k x is the increment of the forward arc length; k y k , z k The coordinates of the three-dimensional centerline of the borehole are given.

[0023] In one possible design of the first aspect, the inertial data includes acceleration data, and the method for reconstructing the three-dimensional centerline trajectory of the borehole further includes:

[0024] Determine whether the acceleration modulus of the measuring probe is close to the gravitational acceleration g;

[0025] If not, then the rotation matrix R is corrected using the gravity direction g0 of the reconstructed coordinate system {W} based on the trajectory. k .

[0026] In one possible design approach of the first aspect, the method for reconstructing the three-dimensional centerline trajectory of the borehole further includes:

[0027] According to the aforementioned forward arc length s k and the borehole direction vector d k Calculate the discrete curvature vector K k :

[0028] Where, d k+1 Position s of arc length k+1 The direction vector of the borehole at that location.

[0029] Determine whether the change in the discrete curvature vector satisfies a preset condition:

[0030] Among them, parameters K is determined by the minimum allowable bending radius. k Let K be the discrete curvature vector at step k. k+1 This is the discrete curvature vector at step k+1;

[0031] If not, use the constructed attitude self-correction objective function to correct the rotation matrix:

[0032] in, These are weighting parameters used to balance inertial information and geometric constraints. R is the angular velocity. k Let R be the rotation matrix at step k. k+1 Let be the rotation matrix for the (k+1)th step.

[0033] In one possible design approach of the first aspect, the method for reconstructing the three-dimensional centerline trajectory of the borehole further includes:

[0034] The obtained inertial data is calibrated and compensated, wherein the angular velocity compensation model is as follows:

[0035] Where, ω k This is the original angular velocity measurement value; The compensated angular velocity; Zero bias for the gyroscope; This is the scaling factor matrix;

[0036] The acceleration compensation model is as follows:

[0037] in, These are the original acceleration measurements; The acceleration after compensation; To achieve zero bias in the accelerometer; This is the accelerometer scale factor matrix.

[0038] In one possible design approach of the first aspect, the method for reconstructing the three-dimensional centerline trajectory of the borehole further includes:

[0039] The calibrated and compensated inertial data is then subjected to low-pass filtering or moving average processing.

[0040] Secondly, a measurement probe for reconstructing the three-dimensional centerline trajectory of a borehole is provided. When the measurement probe travels within the borehole, its axial direction is always aligned with the local axis of the borehole. The measurement probe includes an inertial measurement module and an arc length measurement module. The inertial measurement module measures inertial data reflecting the probe's attitude, and the arc length measurement module measures the forward arc length of the measurement probe along its axial direction. The measurement probe also includes a data processing module, which is used to: obtain an attitude recursive result based on a constructed attitude evolution model reflecting the change in the probe's attitude with the forward arc length; obtain a borehole orientation vector based on the attitude recursive result; and recursively obtain the three-dimensional centerline trajectory of the borehole using the forward arc length, the borehole orientation vector, and the initial position of the three-dimensional centerline of the borehole at the forward arc length. Attached Figure Description

[0041] To more clearly illustrate the technical solutions in the embodiments of this application, the drawings used in the description of the embodiments or related technologies will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0042] Figure 1 This is a schematic diagram of the borehole trajectory measuring device provided in the embodiments of this application;

[0043] Figure 2 This is a cross-sectional view of the axially restricted mechanical support module provided in the embodiments of this application;

[0044] Figure 3 This is a flowchart of the three-dimensional centerline trajectory reconstruction method for boreholes provided in the embodiments of this application;

[0045] Figure 4 This is a three-dimensional centerline trajectory diagram of the borehole provided in the embodiments of this application. The dashed line represents the designed borehole, and the solid line represents the measured actual borehole trajectory. Detailed Implementation

[0046] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0047] It should be noted that although functional modules are divided in the device schematic diagram and a logical order is shown in the flowchart, in some cases, the steps shown or described may be performed in a different order than the module division in the device or the order in the flowchart. The terms "first," "second," etc., in the specification, claims, and the aforementioned drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence.

[0048] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. The terminology used herein is for the purpose of describing embodiments of this application only and is not intended to limit this application.

[0049] The purpose of this embodiment is to provide a method and device for reconstructing the three-dimensional centerline trajectory of underground boreholes based on arc length-constrained inertial field self-correction. By introducing the borehole as a physical constraint condition for a continuous spatial curve, the method achieves accurate reconstruction of the three-dimensional trajectory of underground boreholes without external reference.

[0050] (I) Overall Technical Approach:

[0051] This embodiment does not directly measure the absolute position of the probe in space, but reconstructs the borehole trajectory through the following technical concept:

[0052] By using mechanical structure constraints, the axial direction of the measuring probe is always aligned with the local axis of the borehole;

[0053] Based on the inertial measurement unit, information on the change of probe attitude along the borehole arc length direction is obtained;

[0054] An attitude evolution model is constructed using the borehole arc length as the independent variable to avoid time-domain integration errors.

[0055] A physical prior constraint on the continuity of borehole curvature is introduced to self-correct the inertial measurement results;

[0056] Spatial integration is performed on the corrected directional field to generate the three-dimensional centerline trajectory of the borehole.

[0057] (II) Equipment Technical Solution:

[0058] like Figure 1 As shown, the borehole trajectory measuring device, also known as the measuring probe, in this embodiment includes:

[0059] 1. Inertial Measurement Module:

[0060] The device includes a three-axis gyroscope and a three-axis accelerometer to acquire angular velocity and acceleration information of the measuring probe, but does not include a magnetometer.

[0061] 2. Axially confined mechanical support module (outside the pipe wall, close to the pipe wall):

[0062] Located on the outer periphery of the measuring probe, it includes multiple radial elastic supports to keep the measuring probe centered within the borehole and to restrict its direction of movement, ensuring that the axial direction of the measuring probe is always consistent with the local axis of the borehole.

[0063] 3. Arc length metering module (on the pipe wall):

[0064] The arc length measurement module is used to measure the forward arc length of the measuring probe along the borehole axis. The arc length measurement module can be a rolling encoder wheel, a push rod encoder, or other equivalent structures.

[0065] 4. Data Acquisition and Storage Module:

[0066] Used for synchronous acquisition, time stamping, and storage of inertial measurement data and arc length data.

[0067] 5. Power supply module:

[0068] Provide power to the above modules.

[0069] 6. Data Processing Module:

[0070] It is used to solve and analyze the collected inertial measurement data and arc length data, and output the three-dimensional trajectory of the borehole.

[0071] In practice, the device contains a tightly packed circuit board that integrates inertial sensors, a processor, memory, and a battery. Holes are drilled or brackets are added at specific locations on the tube wall to mount encoding wheels (for arc length measurement), with the wheel surface slightly higher than the tube wall surface. On the outside of the tube, a set of radially elastic supports (such as three sets of spring arms distributed at 120 degrees) are installed at intervals along the axial direction. These support arms extend outwards, with a diameter slightly larger than the borehole diameter, using elastic force to "push" the central metal tube at the exact center of the borehole. Signal lines from all external sensors (encoding wheels) pass through a sealed outer casing into the internal circuit board; power lines are distributed from the battery to each node.

[0072] 7. The wall of the blast hole.

[0073] like Figure 2 As shown, the axially restricted mechanical support module 2.1, also known as the radially elastic support, mainly includes the following structure:

[0074] The propulsion mechanism 2.1.2 is mainly responsible for driving the measuring roller 2.1.6 to perform reciprocating linear motion and controlling its contact pressure with the external measured surface, thereby achieving accurate linear position or distance measurement.

[0075] Compression spring 2.1.5: Power source. It is compressed and mounted below the slider, always pushing upwards to provide a continuous expansion force.

[0076] Parallel linkage mechanism 2.1.3: Transmission and guidance. It connects the slider and the roller arm, ensuring that the roller maintains a specific angle (usually perpendicular to the hole wall) during movement, preventing jamming or tilting.

[0077] Guide rail 2.1.1: Constraint path. Restricts the entire mechanism to linear motion only in the radial (vertical) direction to prevent lateral swaying.

[0078] 2.1.6 Measuring roller: Actuating end. It directly contacts the bore wall and transmits mechanical displacement to the encoder.

[0079] Encoder 2.1.4: Sensor. Measures the rotation or displacement of a roller (the encoder is connected to a linkage or roller shaft to monitor the position or rotation of the roller).

[0080] The working principle is as follows:

[0081] When the device is placed into the borehole, and the borehole diameter is less than the maximum extension distance of roller 2.1.6, the borehole wall will prevent the roller from continuing to extend outward.

[0082] Force balance: The bore wall generates a leftward reaction force on roller 2.1.6, which compresses the parallel linkage mechanism 2.1.3, thereby pressing the slider downward, and finally compressing the pressure spring 2.1.5.

[0083] Adaptive fit: The rebound force generated by the spring 2.1.5 after compression will continuously and constantly push the roller 2.1.6 against the hole wall.

[0084] If there is a depression in the hole wall, the spring 2.1.5 extends and pushes the roller 2.1.6 to fill the depression.

[0085] If there are protrusions on the hole wall, the spring 2.1.5 is compressed, allowing the roller 2.1.6 to retract, thus preventing hard impacts that could damage the equipment.

[0086] Encoder 2.1.4 is mounted above linkage mechanism 2.1.3. As roller 2.1.6 moves up and down due to changes in aperture, the angle of parallel linkage mechanism 2.1.3 changes, causing the shaft of encoder 2.1.4 to rotate. Encoder 2.1.4 records this angle change, and the system can then calculate the current aperture size or the radial displacement of the roller, corresponding to the forward arc length.

[0087] After the probe is inserted into the borehole:

[0088] The compression spring 2.1.5 pushes the parallel linkage mechanism 2.1.3 to unfold outward;

[0089] The connecting rod drives the measuring roller 2.1.6 to fit tightly against the hole wall;

[0090] As the probe advances, the roller 2.1.6 rolls along the bore wall, and its rotation is recorded by the encoder 2.1.4, which is then converted into the arc length Δs. k ;

[0091] Meanwhile, this "radial elastic support" ensures that the probe is always centered or attached to the wall, reducing posture errors.

[0092] (iii) Methodological and technical solutions, such as Figure 3 As shown:

[0093] The borehole three-dimensional trajectory reconstruction method in this embodiment includes the following steps:

[0094] Step S1: Initialization;

[0095] The initial attitude of the measuring probe is set at the borehole inlet as the starting reference for trajectory reconstruction.

[0096] Step S2: Advance the measuring probe along the borehole;

[0097] Under the action of the axially restricted mechanical support module, the measuring probe moves forward along the axis of the borehole, and the attitude change of the measuring probe is guided by the borehole shape.

[0098] Step S3: Data Acquisition;

[0099] The following data are collected simultaneously as the measuring probe advances:

[0100] (1) Inertial measurement data corresponding to changes in probe attitude;

[0101] (2) Data on the arc length of the probe advancing along the borehole.

[0102] Step S4: Arc-length domain attitude modeling;

[0103] Using arc length as the independent variable, an attitude evolution model of the measurement probe attitude as a function of arc length is constructed based on inertial measurement data.

[0104] Step S5: Inertial field self-calibration;

[0105] Based on the physical constraint of borehole curvature continuity, the attitude evolution model is corrected to suppress high-frequency attitude drift that does not conform to the physical characteristics of the borehole.

[0106] Step S6: Trajectory generation;

[0107] Based on the corrected attitude information, spatial integration is performed along the borehole axis to generate the three-dimensional centerline trajectory of the borehole.

[0108] Compared with the prior art, this embodiment has at least the following effects:

[0109] 1. It does not rely on satellite positioning systems and is suitable for underground environments;

[0110] 2. Do not use a magnetometer to avoid the influence of magnetic interference on the measurement results;

[0111] 3. It does not depend on the geometry of the borehole wall and is suitable for environments with feature degradation;

[0112] 4. By using arc length constraints and curvature continuity constraints, inertial drift is effectively suppressed;

[0113] 5. It can directly output the three-dimensional centerline trajectory of the blast hole to meet the needs of blasting engineering.

[0114] I. Overall Calculation Logic:

[0115] In this embodiment, the measurement object is a drilled borehole in an underground metal mine with a designed length of 20m. The borehole is in an air environment with smooth walls and no identifiable features. Furthermore, the underground environment has significant magnetic interference, making it impossible to use a magnetometer or satellite positioning system.

[0116] The complete computing chain used in this embodiment is as follows:

[0117] Inertial Measurement Unit (IMU) data + arc length → calibration compensation → noise filtering → arc length domain attitude recursion → gravity low-frequency constraint → attitude self-correction based on curvature continuity constraint → borehole axial direction vector → spatial integration based on arc length → three-dimensional centerline trajectory of borehole.

[0118] Core idea:

[0119] Instead of integrating velocity in the time domain, we integrate direction in the arc length domain and use the borehole as a geometric prior for a continuous spatial curve to self-correct inertial measurement drift.

[0120] II. From raw data to usable physical quantities (based on sampling parameters in the example):

[0121] 2.1 Acquisition and processing of arc length data:

[0122] Arc length measurement module:

[0123] The arc length measurement module is not a specific sensor, but a functional module. Its function is to provide the time-independent true forward distance along the borehole axis under the condition of no external positioning, so as to map the inertial attitude change to the spatial curve reconstruction.

[0124] The arc length measurement module is used to measure the forward arc length of the measuring probe along the borehole axis. It can be a borehole wall contact rolling structure, a propulsion mechanism displacement measurement structure, or other devices that can equivalently obtain arc length information.

[0125] Hole wall contact type rolling encoder wheel: Structural components include one or more rollers, the rollers making elastic contact with the hole wall, and a rotary encoder connected to the roller shaft.

[0126] The working principle is as follows: probe advances → roller rolls; roller rotates → encoder pulse.

[0127] Calculate the forward arc length based on the wheel circumference. ,in, For the roller rotation angle; The circumference of the roller;

[0128] In this embodiment: borehole design length: 20m; arc length sampling step: 0.01m; number of arc length sampling points k: approximately 2000 points.

[0129] The arc length measurement module outputs a cumulative arc length sequence as the measuring probe advances along the borehole. .

[0130] The arc length increment between adjacent sampling points is:

[0131] Among them, s k Let s be the position of the arc length at step k. k+1 This represents the position of the arc length at step k+1.

[0132] In this embodiment, This step size is significantly smaller than the minimum bending radius that the borehole may exhibit, ensuring that the borehole orientation remains smooth in the discrete domain.

[0133] 2.2 Physical meaning of raw IMU data:

[0134] Coordinate system explanation:

[0135] (1) Probe coordinate system : Fixed to the measuring probe, wherein, The axis is defined as the axial direction of the probe.

[0136] (2) Trajectory Reconstruction Coordinate System : A reference coordinate system used to express the three-dimensional trajectory of the borehole, whose initial orientation is determined by the initial attitude of the probe.

[0137] The inertial measurement module synchronously outputs the following data at each arc-length sampling point:

[0138] (1) Angular velocity data (gyroscope): The angular velocity vector is This indicates that the measuring probe is in its own coordinate system. The instantaneous rotation below.

[0139] (2) Acceleration data (accelerometer): The acceleration vector is In the low-frequency band, it mainly reflects information about the direction of gravity.

[0140] III. Data Preprocessing (in conjunction with underground borehole measurement environment):

[0141] 3.1 IMU Calibration and Error Compensation:

[0142] To avoid the cumulative divergence of attitude error during the 20m arc length integration process, the IMU data is calibrated and compensated.

[0143] (1) The angular velocity compensation model is as follows:

[0144] Where, ω k This is the original angular velocity measurement value; The compensated angular velocity; Zero bias for the gyroscope; This is the scale factor matrix.

[0145] The acceleration data is processed in the same way:

[0146] in, This is the original acceleration; To achieve zero bias in the accelerometer; This is the accelerometer scale factor matrix; This is the acceleration after compensation.

[0147] 3.2 Noise Filtering Processing:

[0148] Considering the disturbances caused by drilling rig vibration, high-frequency motor noise, and contact between mechanical supports and borehole wall during underground drilling, the compensated IMU data is processed by low-pass filtering or moving average.

[0149] The selection of filter parameters follows these principles: the geometric curvature change of the borehole is a low-frequency process, and the high-frequency components mainly come from noise, which should be suppressed.

[0150] IV. Arc-length domain attitude estimation (combined with 2000 arc-length sampling points):

[0151] 4.1 Attitude State Definition:

[0152] Using rotation matrix Indicates the probe attitude and describes the position from the probe coordinate system. To the world coordinate system The transformation relationship. Among them, It is a rotation matrix. It is the "Special Orthogonal Group of dimension 3".

[0153] 4.2 Recursive formula for attitude in arc-length domain:

[0154] Because the propulsion speed is not constant, arc length is used. Replace time as the independent variable for integration.

[0155] The antisymmetric matrix of angular velocity is:

[0156] The attitude recursion formula is:

[0157] This formula represents the measurement probe advancing along the borehole. The cumulative attitude change over time.

[0158] in, This is the increment of arc length; This is the compensated angular velocity vector; The antisymmetric matrix of angular velocity;

[0159] ω x,k ,ω y,k ,ω z,k These are the angular velocity components along the X, Y, and Z axes of the probe coordinate system {B}, respectively. k R is the rotation matrix from the probe coordinate system {B} to the world coordinate system {W} at step k (current attitude); k+1 It is the new pose matrix at step k+1 (after update).

[0160] 4.3 Attitude constraints based on gravity direction:

[0161] Determine if the magnitude of acceleration is close to the gravitational acceleration g. |‖a(k)‖−g|<τ_g

[0162] Check if the current accelerometer modulus is close to the standard gravitational acceleration g (≈9.8 m / s²).

[0163] If the condition is met, i.e. the accelerometer's modulus is close to the standard gravitational acceleration g (≈9.8 m / s²), then the device is considered to be in a quasi-static state (without violent movement or vibration), and the acceleration data can be safely used to estimate the direction of gravity.

[0164] If the conditions are not met (e.g., during accelerated drilling, collision, or vibration), it means that the acceleration contains a large number of non-gravitational components and cannot be used for attitude correction.

[0165] τ_g is the threshold value, which can be set.

[0166] The compensated acceleration is normalized to obtain the unit gravity direction vector. :

[0167] Under the low-frequency assumption, we have:

[0168] in The direction of gravity in the world coordinate system is used as the constraint to suppress the cumulative drift of pitch and roll angles. The compensated acceleration vector; Let be the magnitude of the acceleration vector; The direction vector of unit gravity; It is the transpose of the rotation matrix.

[0169] V. Attitude self-correction based on curvature continuity:

[0170] 5.1 Calculation of borehole orientation vector:

[0171] The axis of the measuring probe is defined in its own coordinate system. The axis, then the position of the arc length. The direction vector of the borehole at that location is :

[0172] in, Position of arc length; It is a rotation matrix; This is the borehole direction vector.

[0173] 5.2 Discrete Curvature Calculation:

[0174] Based on arc length step The discrete curvature vector is defined as:

[0175] Among them, K k It is a discrete curvature vector; Position s of arc length k The borehole direction vector at the location; d k+1 Position s of arc length k+1 The borehole direction vector at the location; The step size is the arc length.

[0176] 5.3 Curvature Continuity Constraint:

[0177] Since underground blast holes cannot have a broken line structure, their curvature changes should remain continuous:

[0178] Among them, K k K k+1 It is a discrete curvature vector; It is determined by the minimum allowable bending radius.

[0179] 5.4 Joint Optimization Model:

[0180] Integrating inertial consistency and curvature continuity, an attitude self-correction objective function is constructed:

[0181] in, These are weighting parameters used to balance inertial information and geometric constraints. R is the angular velocity. k Let R be the rotation matrix at step k. k+1 Let be the rotation matrix for the (k+1)th step.

[0182] This optimization can be achieved through batch least squares or a smoother.

[0183] The output is a set of optimized rotation matrix sequences: , where k = 0, 1, 2, ..., N; The pose sequence to be optimized; It is a rotation matrix; This is the increment of arc length; K is the compensated angular velocity vector. k It is a discrete curvature vector.

[0184] VI. Generation of 3D trajectory of borehole (based on 20 m measured results):

[0185] 6.1 Arc-length domain spatial integration:

[0186] Define the centerline of the borehole in the arc length Location for:

[0187] The initial conditions are set as follows:

[0188] Since the arc length is known and the direction is estimated, the displacement can be obtained directly by integrating the direction:

[0189] in, This is the increment of arc length; Let p be the borehole direction vector. k+1 The centerline of the borehole at arc length s k+1 The location.

[0190] The trajectory exhibits uncertainty due to rigid body transformation, but this does not affect the trajectory shape.

[0191] 6.2 Example of trajectory results (example data):

[0192] Output data format: 3D centerline trajectory of borehole:

[0193] Output characteristics: continuous and smooth, excluding aperture and borehole wall morphology, suitable for blasting analysis and mine modeling.

[0194] Based on the above method, the three-dimensional centerline trajectory of the borehole is obtained, and some of the data is shown in the table below:

[0195] Combination Figure 4 The obvious lateral shift in the rear section can be seen visually.

[0196] VII. Implementation Results and Project Significance

[0197] The three-dimensional trajectory results of the 20m borehole show that the borehole is a continuous spatial curve extending downwards, with obvious lateral offset in the latter half. The end of the borehole is offset by about 1m in the horizontal direction relative to the borehole opening.

[0198] The results are consistent with the common borehole deviation phenomenon in underground mine drilling, verifying the effectiveness of this method under conditions of no satellite positioning, magnetic interference, and no identifiable features inside the borehole.

[0199] This application also provides an electronic device, including: a processor, and a memory coupled to the processor, the memory being used to store a computer program; the processor being used to execute the computer program stored in the memory, so that the electronic device performs the method as described in any of the above embodiments.

[0200] Electronic devices can be computing devices such as desktop computers, laptops, handheld computers, and cloud servers. These electronic devices may include, but are not limited to, processors and memory.

[0201] The processor can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor can be a microprocessor or any conventional processor. The processor is the control center of the electronic device, connecting various parts of the device via various interfaces and lines.

[0202] The memory can be used to store the computer program, and the processor implements various functions of the electronic device by running or executing the computer program stored in the memory and calling the data stored in the memory.

[0203] The memory may primarily include a program storage area and a data storage area. The program storage area may store the operating system, applications required for at least one function, etc.; the data storage area may store data created based on the use of the mobile phone, etc. In addition, the memory may include high-speed random access memory, and may also include non-volatile memory, such as hard disk, memory, plug-in hard disk, smart media card (SMC), secure digital (SD) card, flash card, at least one disk storage device, flash memory device, or other volatile solid-state storage device.

[0204] This application also provides a storage medium, which is a computer-readable storage medium. The computer program is stored in the computer-readable storage medium, and when executed by a processor, the computer program can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable file, or some intermediate form. The computer-readable medium can include: any entity or device capable of carrying the computer program code, a recording medium, a USB flash drive, a portable hard drive, a magnetic disk, an optical disk, a computer memory, a read-only memory (ROM), a random access memory (RAM), an electrical carrier signal, a telecommunication signal, and a software distribution medium, etc.

[0205] This application also provides a computer program product, including: a computer program or instructions that, when the computer program or instructions are run on a computer, cause the computer to perform any of the above possible implementation methods.

[0206] The above description is the preferred embodiment of this application. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of this application, and these improvements and modifications are also considered to be within the scope of protection of this application.

Claims

1. A method for reconstructing the three-dimensional centerline trajectory of a borehole, characterized in that, The method for reconstructing the three-dimensional centerline trajectory of a borehole is based on a measuring probe. When the measuring probe travels through the borehole, its axial direction is always aligned with the local axis of the borehole. The measuring probe is equipped with an inertial measurement module and an arc length measurement module. The method for reconstructing the three-dimensional centerline trajectory of a borehole includes: Obtain inertial data, which reflects the attitude of the measuring probe, measured by the inertial measurement module, and the forward arc length of the measuring probe along the axial direction, measured by the arc length measurement module. Based on the constructed attitude evolution model that reflects the change of the attitude of the measuring probe with the forward arc length, the attitude recursion result is obtained; Based on the attitude recursion result, the borehole direction vector is obtained; and, Using the advance arc length, the borehole direction vector, and the initial position of the borehole three-dimensional centerline at the advance arc length, the trajectory of the borehole three-dimensional centerline is recursively obtained; The probe coordinate system {B} of the measuring probe and the trajectory reconstruction coordinate system {W} of the three-dimensional centerline trajectory of the borehole are connected by a rotation matrix R. k Transformation, where k is the sampling step; The inertial data includes angular velocity data, and the attitude evolution model uses the following attitude recursive formula: Where, ω x,k ,ω y,k ,ω z,k These are the angular velocity components of the X, Y, and Z axes around the probe coordinate system {B}; The antisymmetric matrix of angular velocity; Δs k R is the increment of the forward arc length; k R is the rotation matrix from the probe coordinate system {B} to the trajectory reconstruction coordinate system {W} at step k; k+1 For step k+1, the rotation matrix from the probe coordinate system {B} to the trajectory reconstruction coordinate system {W} is the rotation matrix. Forward arc length s k The borehole direction vector d at the location k for: Among them, R k For step k, the rotation matrix from the probe coordinate system {B} to the trajectory reconstruction coordinate system {W}; The position of the three-dimensional centerline of the borehole at the advance arc length is obtained recursively in the following manner: Where, p k At step k, the three-dimensional centerline of the borehole is at the advancing arc length s k The location of the p; k+1 At step k+1, the three-dimensional centerline of the borehole is at the advancing arc length s k+1 The location of the place; d k Position s of arc length k The borehole direction vector at the location; Δs k x is the increment of the forward arc length; k y k , z k The coordinates of the three-dimensional centerline of the borehole are given.

2. The method for reconstructing the three-dimensional centerline trajectory of a borehole as described in claim 1, characterized in that, The inertial data includes acceleration data, and the method for reconstructing the three-dimensional centerline trajectory of the borehole further includes: Determine whether the acceleration modulus of the measuring probe is close to the gravitational acceleration g. If not, then the rotation matrix R is corrected using the gravity direction g0 of the reconstructed coordinate system {W} based on the trajectory. k .

3. The method for reconstructing the three-dimensional centerline trajectory of a borehole as described in claim 1, characterized in that, The method for reconstructing the three-dimensional centerline trajectory of boreholes also includes: According to the aforementioned forward arc length s k and the borehole direction vector d k Calculate the discrete curvature vector K k : Where, d k+1 Position s of arc length k+1 The borehole direction vector at that location. Determine whether the change in the discrete curvature vector satisfies a preset condition: Among them, parameters K is determined by the minimum allowable bending radius. k Let K be the discrete curvature vector at step k. k+1 Let be the discrete curvature vector at step k+1. If not, use the constructed attitude self-correction objective function to correct the rotation matrix: in, These are weighting parameters used to balance inertial information and geometric constraints. R is the angular velocity. k+1 Let be the rotation matrix for the (k+1)th step.

4. The method for reconstructing the three-dimensional centerline trajectory of a borehole as described in claim 1, characterized in that, The method for reconstructing the three-dimensional centerline trajectory of boreholes also includes: The obtained inertial data is calibrated and compensated, wherein the angular velocity compensation model is as follows: Where, ω k This is the original angular velocity measurement value; The compensated angular velocity; Zero bias for the gyroscope; This is the scale factor matrix. The acceleration compensation model is as follows: in, These are the original acceleration measurements; The acceleration after compensation; To achieve zero bias in the accelerometer; This is the accelerometer scale factor matrix.

5. The method for reconstructing the three-dimensional centerline trajectory of a borehole as described in claim 4, characterized in that, The method for reconstructing the three-dimensional centerline trajectory of boreholes also includes: The calibrated and compensated inertial data is then subjected to low-pass filtering or moving average processing.

6. A measuring probe for reconstructing the three-dimensional centerline trajectory of a borehole, characterized in that, As the measuring probe travels through the borehole, its axial direction is always aligned with the local axis of the borehole. The measuring probe includes an inertial measurement module and an arc length measurement module. The inertial measurement module measures inertial data reflecting the probe's attitude, and the arc length measurement module measures the forward arc length of the measuring probe along its axial direction. The measuring probe also includes a data processing module, which is used to: obtain an attitude recursion result based on a constructed attitude evolution model reflecting the probe's attitude change with the forward arc length; obtain the borehole direction vector based on the attitude recursion result; and recursively obtain the borehole three-dimensional centerline trajectory using the forward arc length, the borehole direction vector, and the initial position of the borehole's three-dimensional centerline at the forward arc length. The probe coordinate system {B} of the measuring probe and the trajectory reconstruction coordinate system {W} of the borehole's three-dimensional centerline trajectory are connected by a rotation matrix R. k Transformation, where k is the sampling step; The inertial data includes angular velocity data, and the attitude evolution model uses the following attitude recursive formula: Where, ω x,k ,ω y,k ,ω z,k These are the angular velocity components of the X, Y, and Z axes around the probe coordinate system {B}; The antisymmetric matrix of angular velocity; Δs k R is the increment of the forward arc length; k R is the rotation matrix from the probe coordinate system {B} to the trajectory reconstruction coordinate system {W} at step k; k+1 For step k+1, the rotation matrix from the probe coordinate system {B} to the trajectory reconstruction coordinate system {W} is the rotation matrix. Forward arc length s k The borehole direction vector d at the location k for: Among them, R k For step k, the rotation matrix from the probe coordinate system {B} to the trajectory reconstruction coordinate system {W}; The position of the three-dimensional centerline of the borehole at the advance arc length is obtained recursively in the following manner: Where, p k At step k, the three-dimensional centerline of the borehole is at the advancing arc length s k The location of the p; k+1 At step k+1, the three-dimensional centerline of the borehole is at the advancing arc length s k+1 The location of the place; d k Position s of arc length k The borehole direction vector at the location; Δs k x is the increment of the forward arc length; k y k , z k The coordinates of the three-dimensional centerline of the borehole are given.

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