A method for calculating a drilling attitude based on a MIMU

Abstract

This invention discloses a MIMU-based method for calculating drilling attitude. During drilling, real-time data on triaxial acceleration, triaxial angular velocity, triaxial magnetic field strength, and temperature are collected. Temperature drift compensation is applied to the collected data, and the quaternion derivatives of the gyroscopes are calculated. Using accelerometer and magnetometer data, the gradient directions of the accelerometers and magnetometers are calculated using a gradient descent algorithm. A motion confidence factor is introduced using a Logistic function to control the weights of the accelerometers and magnetometers. The corrected gradients are fused and fed back into the quaternion update equation, combined with the quaternion derivatives predicted by the gyroscopes, and finally, the updated quaternions are used to calculate the three-dimensional attitude of the drilling tool—azimuth angle ψ, inclination angle θ, and tool face angle.

Description

Technical Field

[0001] This invention relates to a method for calculating drilling attitude based on MIMU. Background Technology

[0002] With the rapid development of the industrial economy, the amount of resources extracted and their demand are constantly increasing. There is a need to improve the efficiency of resource exploration and extraction within a limited timeframe, which relies heavily on high-precision drill string attitude information. The accuracy of the drill string's inclination angle, azimuth angle, and tool face angle attitude information determines whether drilling can proceed smoothly, efficiently, and safely on schedule. However, the measurement-while-drilling environment is often complex and diverse. During drilling, factors such as vibration and magnetic interference may adversely affect the output information of the inertial measurement unit (MIMU), leading to significant errors in the drill string attitude angle information (inclination angle, tool face angle, and azimuth angle). Failure to properly integrate this multi-source information will severely impact the stability and accuracy of the measurement.

[0003] Currently, commonly used methods for downhole attitude estimation include complementary filtering and extended Kalman filtering (EKF). Theoretically, these methods can fuse multi-sensor data to estimate drill string attitude. However, they have significant shortcomings when applied to downhole measurement-while-drilling (MWD) instruments in harsh downhole environments with limited computational resources: complementary filtering, while computationally inexpensive and easy to implement, relies on empirical adjustments of its filter coefficients, has limited dynamic response performance, and is prone to significant drift and accumulated errors under strong vibrations and shocks; while extended Kalman filtering theoretically offers higher accuracy, its algorithmic complexity is high, consuming enormous computational resources, and it is highly sensitive to sensor noise models and initial states, making it difficult to guarantee real-time and stable operation in the confined space and limited processing capabilities of embedded systems downhole. This invention proposes a MIMU-based MWD attitude estimation method. This algorithm boasts high computational efficiency, easily adjustable parameters, and extremely low computational resource requirements. It effectively fuses MIMU data to suppress gyroscope drift, making it particularly suitable for achieving rapid, stable, and high-precision real-time drill string attitude measurement on resource-constrained downhole MWD instruments, providing a reliable basis for precise guidance control. Summary of the Invention

[0004] The purpose of this invention is to provide a drilling attitude calculation method based on MIMU.

[0005] During the drilling process, the nine-axis motion parameters consisting of three-axis acceleration, three-axis angular velocity, and three-axis magnetic field are collected in real time. The three-dimensional attitude angles (inclination angle, azimuth angle, and tool face angle) of the drill string in the geographic reference coordinate system are accurately calculated by the drilling attitude calculation method. Through coordinate system transformation, the wellbore trajectory change rate and guidance accuracy are quantitatively evaluated.

[0006] The aforementioned MIMU-based drilling attitude calculation method specifically includes the following calculation steps.

[0007] Step 1: Collect triaxial acceleration, triaxial angular velocity, triaxial magnetic field strength and temperature information, and perform temperature drift compensation on the collected data.

[0008] Step 2: Calculate the quaternion derivative of the gyroscope. Using accelerometer and magnetometer data, calculate the gradient direction of the accelerometer and magnetometer using the gradient descent algorithm.

[0009] Step 3: Introduce motion confidence factors using the Logistic function. ,pass Control the weights of the accelerometer and magnetometer.

[0010] Step 4: After fusing and correcting the gradient, it is fed back into the quaternion update equation and combined with the quaternion derivative predicted by the gyroscope.

[0011] Step 5: Use the updated quaternions to calculate the three-dimensional attitude of the drill string—azimuth, inclination angle, and tool face angle.

[0012] In drilling attitude measurement, the three-dimensional attitude parameters include: azimuth angle ψ, inclination angle θ, and tool face angle. The well inclination angle measures the degree of inclination of the drill string relative to the horizontal direction during drilling; the tool face angle indicates the direction of inclination of the drill string during drilling; and the azimuth angle measures the degree of deviation of the drill string from the horizontal plane during drilling.

[0013] We select geographic coordinate system n as the reference coordinate system (Northeast-Sky coordinate system). The reference coordinate system is... (n-system), the origin of the coordinate system is chosen to be on the Earth's surface, and the line connecting the Earth's center and the origin is set as... The axis points towards the sky; The axis faces north; Facing east, the three coordinate axes point in accordance with the right-hand rule.

[0014] The measurement coordinate system is (B-frame), establish the measurement coordinate system along the three coordinate axes of the drill string, with the center of gravity of the drill string as the origin of the B-frame. shaft and The axes are orthogonal to each other within the drill bit's reference plane. The shaft is along the axis of the drill string and perpendicular to it. shaft and The plane formed by the axes, the nine-axis sensor is fixedly mounted on the drill bit and is orthogonal to the three axes of the drill bit.

[0015] The transformation matrix from the n-system to the b-system is First rotate around the Z-axis by an angle Let be the azimuth angle, then rotate it around the Y-axis by an angle θ, which is the inclination angle, and finally rotate it around the x-axis by an angle. Let be the tool face angle; the rotation matrices corresponding to these three rotation angles are:

[0016] The attitude matrix can be obtained as follows:

[0017] Describing rotation matrices using quaternions for:

[0018] In step 2, the quaternion derivative of the gyroscope is calculated. Using accelerometer and magnetometer data, the gradient directions of the accelerometer and magnetometer are calculated using the gradient descent algorithm. Angular velocity measured by gyroscope Used to calculate the derivative of a quaternion:

[0019] continuous time derivative Discretized using the forward Euler method, we obtain ,in Angular velocity, , and ω represents the angular velocity along the x, y, and z axes, respectively. Let q be the first-order differential of a quaternion. Let t be the new quaternion for time t (updated by angular velocity), where t is the sampling time. The sampling period.

[0020] Integrating the gyroscope alone will accumulate errors, so an accelerometer is needed to provide a gravity direction reference. The gradient descent algorithm is then used to integrate the accelerometer data. This is used to correct the attitude quaternion and compensate for the integral drift of the gyroscope.

[0021] Gravity objective function:

[0022] Its Jacobian matrix is:

[0023] To reduce error, the quaternion is updated along the negative gradient direction, where the gradient direction is: Where a is acceleration, These are the accelerations along the x, y, and z axes, respectively.

[0024] Gyroscope integration causes tool face angle drift, and since accelerometers cannot correct for tool face angle, a magnetometer is used to measure the direction of the Earth's magnetic field as an absolute reference. The magnetometer was calibrated using gradient descent: Magnetometer objective function:

[0025] Its Jacobian matrix is:

[0026] The gradient direction is: Where m is the magnetic field strength, , respectively, represent the magnetic field strength along the x, y, and z axes. , is the geomagnetic field reference vector, obtained through static calibration. These are the reference magnetic field strengths along the x-axis and z-axis, respectively.

[0027] In step 3, the Logistic function is used to introduce the motion confidence factor. ,pass Controlling the weights of the accelerometer and magnetometer: Accelerometers are susceptible to non-gravitational acceleration interference during motion, magnetometers are prone to distortion in environments with strong magnetic interference, and gyroscopes are prone to integral drift during long-term operation. A motion confidence factor is calculated to address these issues. This is to control the level of participation of each sensor. Where k is the attenuation steepness control factor, and k=10 is taken in... The interval completes the main attenuation, where c is the midpoint of the function. Taking c=0.2, the test shows that 0.2g is the reliability inflection point in the measurement while drilling. When the motion acceleration > 0.2g, the sensor reliability decreases significantly. The accelerometer measures the difference between the resultant acceleration and the gravitational acceleration. This is the acceleration due to gravity.

[0028] Acceleration weights: When at rest or in low-speed motion, , A larger value indicates a higher level of confidence in the accelerometer data, and a higher weighting for the accelerometer; the more severe the drill string shaking is under interference, the greater the impact. The larger, μ Decreasing the weighting indicates a lower level of confidence in the accelerometer data, thereby reducing the weight of the accelerometer data in attitude calculation and reducing errors.

[0029] Magnetometer weight: ,in It is the magnetic field stability factor. This is a reference value for the local magnetic field strength. It is the current magnetic field strength magnetic field strength at the previous moment The difference between them; introducing a magnetic field stability factor. The weights can be dynamically adjusted based on the rate of change of the magnetometer data; when the magnetic field is stable, When the value is close to 1, the magnetometer has a relatively large weight; under magnetic field interference, Reduce the magnetometer weight to minimize interference.

[0030] After fusing and correcting the gradient in step 4, it is fed back into the quaternion update equation and combined with the quaternion derivative predicted by the gyroscope, specifically including: The calibration gradients from the accelerometer and magnetometer are fused: accelerometer gradient The main corrections are for gravity direction (inclination and azimuth) and magnetometer gradient. The primary function is to correct for geomagnetic direction (tool face angle). In measurements while drilling, this can simultaneously correct for attitude errors caused by drill string vibration and rotation. The gradient magnitude may vary under different attitudes (e.g., the gradient increases during rapid movement), therefore, it needs to be normalized. .

[0031] To correct gyroscope drift in real time, it is necessary to combine the attitude change obtained by integrating the gyroscope (high frequency but prone to drift) with the correction amount obtained by gradient descent (low frequency but stable): , among which It is the first-order differential of the quaternion after fusion. This is the fusion coefficient, used to control the weight of the correction term.

[0032] The fused derivative Quaternions are updated discretely using the Euler method. ,in After discretization, the attitude quaternion at the current time k is obtained. This is the attitude quaternion at the next time step k+1 after discretization. Due to numerical integration and computational errors, the quaternion may no longer be a unit quaternion. To maintain the accuracy of the attitude representation and avoid errors introduced by changes in the quaternion's modulus, normalization is required. This is to ensure that it still represents rotation.

[0033] Furthermore, in step 5, the updated quaternions are used to calculate the three-dimensional attitude of the drill string—azimuth angle ψ, inclination angle θ, and tool face angle. .

[0034]

[0035] This solution method is highly efficient, has easily adjustable parameters, requires low computational resources, and can effectively fuse data to suppress drift, thereby achieving fast, stable, and high-precision real-time monitoring of drill bit attitude. Attached Figure Description

[0036] Figure 1 This is the definition of the drill coordinate system in this invention.

[0037] Figure 2 This is a flowchart of the drilling attitude calculation method of the present invention. Detailed Implementation

[0038] The purpose of this invention is to accurately calculate the three-dimensional attitude angles (inclination angle, azimuth angle, and tool face angle) of the drill bit in the geographic reference coordinate system by real-time acquisition of triaxial acceleration, triaxial angular velocity, and triaxial magnetic field strength during the drilling process and by using the drilling attitude calculation method. This reduces the susceptibility of accelerometers and magnetometers to instantaneous impacts or magnetic interference.

[0039] In drilling attitude measurement, the three-dimensional attitude parameters include: azimuth angle ψ, inclination angle θ, and tool face angle. ,like Figure 1 The coordinate system for measurement while drilling is shown, where H represents the ground, V represents the borehole plane, and P represents the cross section of the drill string. The inclination angle measures the degree of inclination of the drill string relative to the horizontal direction during drilling; the tool face angle indicates the direction of inclination of the drill string during drilling; and the azimuth angle measures the degree of deviation of the drill string from the horizontal plane during drilling.

[0040] We select geographic coordinate system n as the reference coordinate system (Northeast-Sky coordinate system). The reference coordinate system is... (n-system), the origin of the coordinate system is chosen to be on the Earth's surface, and the line connecting the Earth's center and the origin is set as... The axis points towards the sky; The axis faces north; Facing east, the three coordinate axes point in accordance with the right-hand rule.

[0041] The measurement coordinate system is (B-frame), establish the measurement coordinate system along the three coordinate axes of the drill string, with the center of gravity of the drill string as the origin of the B-frame. shaft and The axes are orthogonal to each other within the drill bit's reference plane. The shaft is along the axis of the drill string and perpendicular to it. shaft and The sensor is fixedly mounted on the drill bit in a plane formed by the axes, and is orthogonal to the three axes of the drill bit.

[0042] The transformation matrix from the n-system to the b-system is First rotate around the Z-axis by an angle Let be the azimuth angle, then rotate it around the Y-axis by an angle θ, which is the inclination angle, and finally rotate it around the x-axis by an angle. Let be the tool face angle. The rotation matrices corresponding to these three rotation angles are:

[0043] The attitude matrix can be obtained as follows:

[0044] Describing rotation matrices using quaternions for:

[0045] A flowchart of a MIMU-based drilling attitude calculation method is shown below. Figure 2 As shown.

[0046] First, the quaternion derivative of the gyroscope is calculated. Then, using accelerometer and magnetometer data, the gradient directions of the accelerometer and magnetometer are calculated using the gradient descent algorithm. Angular velocity measured by gyroscope Used to calculate the derivative of a quaternion:

[0047] continuous time derivative Discretized using the forward Euler method, we obtain ,in Angular velocity, , and ω represents the angular velocity along the x, y, and z axes, respectively. Let q be the first-order differential of a quaternion. Let t be the new quaternion for time t (updated by angular velocity), where t is the sampling time. The sampling period.

[0048] Integrating the gyroscope alone will accumulate errors, so an accelerometer is needed to provide a gravity direction reference. The gradient descent algorithm is then used to integrate the accelerometer data. This is used to correct the attitude quaternion and compensate for the integral drift of the gyroscope.

[0049] Gravity objective function:

[0050] Its Jacobian matrix is:

[0051] To reduce error, the quaternion is updated along the negative gradient direction, where the gradient direction is: Where a is acceleration, These are the accelerations along the x, y, and z axes, respectively.

[0052] Gyroscope integration causes tool face angle drift, and since accelerometers cannot correct for tool face angle, a magnetometer is used to measure the direction of the Earth's magnetic field as an absolute reference. The magnetometer was calibrated using gradient descent: Magnetometer objective function:

[0053] Its Jacobian matrix is:

[0054] The gradient direction is: Where m is the magnetic field strength, , respectively, represent the magnetic field strength along the x, y, and z axes. , is the geomagnetic field reference vector, obtained through static calibration. These are the reference magnetic field strengths along the x-axis and z-axis, respectively.

[0055] Then, the Logistic function is used to introduce a motion confidence factor. ,pass Controlling the weights of the accelerometer and magnetometer: Accelerometers are susceptible to non-gravitational acceleration interference during motion, magnetometers are prone to distortion in environments with strong magnetic interference, and gyroscopes are prone to integral drift during long-term operation. A motion confidence factor is calculated to address these issues. This is to control the level of participation of each sensor. Where k is the attenuation steepness control factor, and k=10 is taken in... The interval completes the main attenuation; c is the midpoint of the function, and we take c=0.2. Tests show that 0.2g is the reliability inflection point in measurement while drilling. When the motion acceleration > 0.2g, the sensor reliability decreases significantly. The accelerometer measures the difference between the resultant acceleration and the gravitational acceleration. This is the acceleration due to gravity.

[0056] Acceleration weights: When at rest or in low-speed motion, , A larger value indicates a higher level of confidence in the accelerometer data, and a higher weighting for the accelerometer; the more severe the drill string shaking is under interference, the greater the impact. The larger, μ Decreasing the weighting indicates a lower level of confidence in the accelerometer data, thereby reducing the weight of the accelerometer data in attitude calculation and reducing errors.

[0057] Magnetometer weight: ,in It is the magnetic field stability factor. This is a reference value for the local magnetic field strength. It is the current magnetic field strength magnetic field strength at the previous moment The difference between them; introducing a magnetic field stability factor. The weights can be dynamically adjusted based on the rate of change of the magnetometer data, when the magnetic field is stable. When the value is close to 1, the magnetometer has a relatively large weight; under magnetic field interference, Reduce the magnetometer weight to minimize interference.

[0058] After fusing and correcting the gradient, it is fed back into the quaternion update equation, where it is combined with the quaternion derivative predicted by the gyroscope. Specifically, this includes: The calibration gradients from the accelerometer and magnetometer are fused: accelerometer gradient The main corrections are for gravity direction (inclination and azimuth) and magnetometer gradient. The primary function is to correct for geomagnetic direction (tool face angle). In measurements while drilling, this can simultaneously correct for attitude errors caused by drill string vibration and rotation. The gradient magnitude may vary under different attitudes (e.g., the gradient increases during rapid movement), therefore, it needs to be normalized. .

[0059] To correct gyroscope drift in real time, it is necessary to combine the attitude change obtained by integrating the gyroscope (high frequency but prone to drift) with the correction amount obtained by gradient descent (low frequency but stable): , among which It is the first-order differential of the quaternion after fusion. This is the fusion coefficient, used to control the weight of the correction term.

[0060] The fused derivative Quaternions are updated discretely using the Euler method. ,in After discretization, the attitude quaternion at the current time k is obtained. This is the attitude quaternion at the next time step k+1 after discretization. Due to numerical integration and computational errors, the quaternion may no longer be a unit quaternion. To maintain the accuracy of the attitude representation and avoid errors introduced by changes in the quaternion's modulus, normalization is required. This is to ensure that it still represents rotation.

[0061] Finally, in step 5, the updated quaternions are used to calculate the three-dimensional attitude of the drill string—azimuth ψ, inclination angle θ, and tool face angle. .

[0062]

[0063] This solution method is highly efficient, has easily adjustable parameters, requires low computational resources, and can effectively fuse data to suppress drift, thereby achieving fast, stable, and high-precision real-time monitoring of drill bit attitude.

Claims

1. A method for calculating the attitude while drilling based on a MIMU, characterized in that, The following solution steps are included: Step 1: Collect triaxial acceleration, triaxial angular velocity, triaxial magnetic field strength and temperature information, and perform temperature drift compensation on the collected data; Step 2: Calculate the quaternion derivative of the gyroscope. Using accelerometer and magnetometer data, calculate the gradient directions of the accelerometer and magnetometer using the gradient descent algorithm. Step 3: Introducing motion confidence factor using a logistic function by controlling the weight of the accelerometer and magnetometer; Step 4: After fusing and correcting the gradient, feed it back into the quaternion update equation and combine it with the quaternion derivative predicted by the gyroscope; Step 5: Use the updated quaternions to calculate the three-dimensional attitude of the drill string—azimuth ψ, inclination angle θ, and tool face angle φ.

2. The method according to claim 1, wherein, The specific calculation process for steps 2 to 5 is as follows: (1) In step 2, the quaternion derivative of the gyroscope is calculated. Using the accelerometer and magnetometer data, the gradient directions of the accelerometer and magnetometer are calculated using the gradient descent algorithm: ①angular velocity measured by a gyroscope for calculating the quaternion derivative: Continuous-time derivative By Forward Euler discretization where is the angular velocity, , and are the angular velocities of the x, y and z axes respectively, is the quaternion first derivative, q is the quaternion, is the new quaternion at time t (updated from angular velocities), t is the sampling time, is the sampling period; ②Gyroscope alone will accumulate errors, need to provide gravity direction reference accelerometer, using gradient descent algorithm, through the accelerometer data to correct the attitude quaternion, compensate for the drift of gyroscope integration; Gravity objective function: Its Jacobian matrix is: To reduce error, the quaternion is updated along the negative gradient direction, where the gradient direction is: Where a is acceleration, These are the accelerations along the x, y, and z axes, respectively. ③ Gyroscope integration causes tool face angle drift, and since accelerometers cannot correct tool face angle, a magnetometer is used to measure the direction of the Earth's magnetic field as an absolute reference. The magnetometer was calibrated using gradient descent: Magnetometer objective function: Its Jacobian matrix is: The gradient direction is: Where m is the magnetic field strength, , respectively, represent the magnetic field strength along the x, y, and z axes. , is the geomagnetic field reference vector, obtained through static calibration. These are the reference magnetic field strengths along the x-axis and z-axis, respectively. (2) Step 3 uses the Logistic function to introduce the motion confidence factor. ,pass Controlling the weights of the accelerometer and magnetometer: ① Accelerometers are susceptible to non-gravitational acceleration interference during motion, magnetometers are prone to distortion in environments with strong magnetic interference, and gyroscopes are prone to integral drift during long-term operation. A motion confidence factor can be calculated to address this. This is to control the level of participation of each sensor. Where k is the attenuation steepness control factor, and k=10 is taken in... The interval completes the main attenuation; c is the midpoint of the function, and we take c=0.

2. Tests show that 0.2g is the reliability inflection point in measurement while drilling. When the motion acceleration > 0.2g, the sensor reliability decreases significantly. The accelerometer measures the difference between the resultant acceleration and the gravitational acceleration. It is the acceleration due to gravity; ②Acceleration weighting: When at rest or in low-speed motion, , A larger value indicates a higher level of confidence in the accelerometer data, and a higher weighting for the accelerometer; the more severe the drill string shaking is under interference, the greater the impact. The larger the value, the smaller the value of μ, indicating a lower level of confidence in the accelerometer data. This reduces the weight of the accelerometer data in attitude calculation and reduces errors. ③ Magnetometer weight: ,in It is the magnetic field stability factor. This is a reference value for the local magnetic field strength. It is the current magnetic field strength magnetic field strength at the previous moment The difference between them; introducing a magnetic field stability factor. The weights can be dynamically adjusted based on the rate of change of the magnetometer data, when the magnetic field is stable. When the value is close to 1, the magnetometer has a relatively large weight; under magnetic field interference, Reduce the magnetometer weight to minimize interference. (3) After fusing and correcting the gradient in step 4, it is fed back into the quaternion update equation and combined with the quaternion derivative predicted by the gyroscope. Specifically, it includes: ① Fuse the correction gradients from the accelerometer and magnetometer: accelerometer gradient The main corrections are for gravity direction (well inclination and azimuth angle) and magnetometer gradient. The primary function is to correct for geomagnetic direction (tool face angle). In measurements while drilling, this can simultaneously correct for attitude errors caused by drill string vibration and rotation. The gradient magnitude may vary under different attitudes (e.g., the gradient increases during rapid movement), therefore, it needs to be normalized. ; ② To correct gyroscope drift in real time, it is necessary to combine the attitude change obtained by integrating the gyroscope (high frequency but prone to drift) with the correction amount obtained by gradient descent (low frequency but stable): ,in It is the first-order differential of the quaternion after fusion. This is the fusion coefficient, used to control the weight of the correction term; ③ The fused derivative Quaternions are updated discretely using the Euler method. ,in After discretization, the attitude quaternion at the current time k is obtained. This is the attitude quaternion at the next time step k+1 after discretization. Due to numerical integration and computational errors, the quaternion may no longer be a unit quaternion. To maintain the accuracy of the attitude representation and avoid errors introduced by changes in the quaternion's modulus, normalization is required. To ensure that it still represents rotation; (4) Step 5 uses the updated quaternion to calculate the three-dimensional attitude of the drill string—azimuth ψ, inclination angle θ, and tool face angle φ.

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