Thick-Tail Measurement Noise Filtering Model and Establishment Method for Near-Bit Measurement-While-Drilling System

Abstract

The present invention discloses a thick-tailed measurement noise filtering model and a method for establishing the same for a near-bit measurement-while-drilling system, belonging to the technical field of near-bit measurement-while-drilling systems, including: establishing a posterior probability density function distribution model of sensor measurement noise; completing the estimation of unknown states, scale matrices, and degrees of freedom parameters of sensor measurement noise; and establishing a new filter and smoother for sensor thick-tailed measurement noise. By the above means, the present invention designs a new filter and smoother model for thick-tailed measurement noise to improve the measurement accuracy of the near-bit measurement-while-drilling system by establishing a posterior probability density function distribution model of sensor measurement noise, estimating unknown states, scale matrices, and degrees of freedom parameters of sensor measurement noise, and establishing a new filter and smoother for sensor thick-tailed measurement noise. It solves the problem that the colored thick-tailed measurement noise induced by measurement outliers in the near-bit measurement-while-drilling system cannot use a filter with a traditional standard Gaussian distribution.

Description

Technical Field

[0001] The present invention relates to the technical field of near-bit measurement-while-drilling systems, and particularly to a thick-tailed measurement noise filtering model and a method for establishing the same for a near-bit measurement-while-drilling system. Background Art

[0002] In recent years, MEMS sensors (Microelectro Mechanical Systems) that have developed rapidly have the advantages of small size, light weight, low price, strong anti-vibration and shock resistance, high reliability, etc., making measurement-while-drilling based on MEMS inertial technology the best alternative to fiber optic gyroscopes and flexible accelerometers and receiving extensive attention. However, since the near-bit measurement-while-drilling system in the coalbed methane wellbore has been suffering from high-dynamic rotation of the drill string and strong vibration and shock during operation, the MEMS sensor introduces additional complex measurement noise while measuring the motion state information of the drill bit near the bit, which in turn leads to large errors in attitude calculation and greatly reduces the measurement accuracy of the drilling trajectory.

[0003] The colored thick-tailed measurement noise induced by measurement outliers of the near-bit MEMS measurement-while-drilling system cannot use filters with traditional standard Gaussian distributions, which has a great impact on the measurement accuracy of the near-bit measurement-while-drilling system. Designing an error estimation model for the colored thick-tailed measurement noise of the coalbed methane near-bit MEMS measurement-while-drilling system is of great significance for improving the measurement accuracy.

[0004] Based on this, the present invention designs a thick-tailed measurement noise filtering model and a method for establishing the same for the near-bit measurement-while-drilling system to solve the above problems. Summary of the Invention

[0005] In view of the above-mentioned drawbacks of the prior art, the present invention provides a thick-tailed measurement noise filtering model and a method for establishing the same for a near-bit measurement-while-drilling system.

[0006] To achieve the above objectives, the present invention is realized through the following technical solutions:

[0007] A method for establishing a thick-tailed measurement noise filtering model for a near-bit measurement-while-drilling system includes the following steps:

[0008] S1: Analyze the influence characteristics of the drill string impact vibration factors caused by the drill bit cutting the coal seam on the accelerometer in the near-bit measurement-while-drilling system, and at the same time analyze the interference characteristics of ferromagnetic substances in the drill string and the coal seam on the fluxgate in the measurement-while-drilling system;

[0009] S2: The measurement noise-induced measurement outlier characteristics of the accelerometer and fluxgate in the near-bit measurement-while-drilling system under shock vibration and complex magnetic field interference are studied. Further explore the heavy-tailed measurement noise characteristics of the near-bit measurement-while-drilling system caused by sensor measurement outliers, and establish a Student's T distribution model under the posterior probability density function;

[0010] S3: Establish the probability density function of the conjugate prior distribution of the unknown parameters and the state to be estimated, and use the variational Bayesian method to update the posterior probability density functions of the state, scale matrix, and degree-of-freedom parameters to Gaussian, inverse Wishart, and Gamma distributions respectively, and estimate the unknown state, scale matrix, and degree-of-freedom parameters at the same time;

[0011] S4: Combine the state extension method and the variational Bayesian method to find an approximate solution of the joint posterior filtering probability density function;

[0012] S5: Establish a robust Gaussian approximation filter and a robust Gaussian approximation smoother model with colored heavy-tailed measurement noise, and realize the accurate calculation of updating the state, scale matrix, and degree-of-freedom parameters of the coalbed methane near-bit measurement-while-drilling system.

[0013] Furthermore, in step S2, the Student's T distribution model under the posterior probability density function is determined by the Gaussian approximate state estimation, induced measurement outliers, and heavy-tailed measurement noise on the basis of continuously measuring the gravity field and geomagnetic field parameters of the downhole instrument state by using the gravity accelerometer and fluxgate.

[0014] Furthermore, the Gaussian approximate state estimation is determined by the following formula:

[0015] x k =f k-1 (x k-1 )+q k-1 ;

[0016] Z k =h k (x k )+e k ;

[0017] In the formula, k represents the discrete time series, 0 ≤ k ≤ M, M is any moment, x k represents the set of all state vectors from time 0 to time M, z k represents the set of all measurement vectors from time 1 to time M, f k-1 (x k-1 ) and h k (x k ) are arbitrary known functions, q k and ek are the system noise and the measurement noise respectively; q k is Gaussian white noise, e k is colored heavy-tailed noise.

[0018] Furthermore, the colored heavy-tailed noise is determined by the following formula:

[0019] e k = Ψ k-1 e k-1 + ξ k-1 ;

[0020] In the formula, Ψ k-1 is a known correlation parameter; ξ k is white heavy-tailed noise.

[0021] Furthermore, the Student’s t distribution model is determined by the following formula:

[0022]

[0023] In the formula, t(ξ k ; 0, R, v) represents the Student’s t probability density function with a mean of 0, a scale matrix of R, and a degrees of freedom parameter of v, represents the Gaussian probability density function with a mean of 0 and a variance of ; represents the Gamma probability density function, and λ k is an auxiliary random variable.

[0024] Furthermore, in step S3, the inverse Wishart and Gamma distributions are determined by the following formula:

[0025] Inverse Wishart probability density function: Wt(R; u 0 , U 0 );

[0026] In the formula, u 0 represents the degrees of freedom parameter of the inverse Wishart probability density function, and U 0 represents the inverse scale matrix of the inverse Wishart probability density function;

[0027] Gamma probability density function:

[0028] Furthermore, the probability density function of the conjugate prior distribution is determined by the following formula:

[0029]

[0030] In the formula, Wt(R; u 0 , U0 ) represents that the degree - of - freedom parameter is u 0 , and the inverse - scale matrix is U 0 of the inverse Wishart probability density function; the initial state x 0 is a Gaussian random vector with mean and covariance matrix being and P 0|0 respectively; and the initial state x 0 , the system noise q k , the measurement noise e k are mutually independent. is a Gaussian probability density function with mean and covariance matrix being and P 0|0 respectively; G(v; a 0 , b 0 ) represents the Gamma probability density function with shape parameter a 0 and rate parameter b 0 respectively.

[0031] Furthermore, in step S3, it also includes: whitening the colored measurement parameters by using the measurement - difference method, through the following formula:

[0032] b k = Z k - Ψ k-1 Z k-1 ;

[0033] In the formula, b k is the re - constructed white measurement.

[0034] Furthermore, in step S4, the extended state vector is obtained through the following formula:

[0035] δ k := [x k x k-1 T ;

[0036] where, δ k is the extended state vector.

[0037] The present invention also provides a thick - tailed measurement - noise filtering model of a near - bit measurement - while - drilling system constructed by the described establishment method.

[0038] Beneficial effects

[0039] ​The present invention comprehensively analyzes the working state of a coalbed methane oriented drilling device, studies the measurement noise characteristics of thick tails induced by measurement outliers generated by accelerometers and fluxgate sensors in a near-bit measurement-while-drilling system due to drill string vibration and magnetic field interference, constructs a Student's T distribution model of the noise characteristics, and simultaneously estimates unknown state, scale matrix, and degree-of-freedom parameters using state extension methods and variational Bayesian methods; studies new robust Gaussian approximation filters and smoothers, and establishes a new non-linear measurement noise filtering model for accelerometer and fluxgate measurements to improve the robustness and measurement accuracy of the sensors.

[0040] The present invention uses an approximate solution of the joint posterior filtering probability density function to establish a robust Gaussian approximation filter and a robust Gaussian approximation smoother model with colored thick-tailed measurement noise, and realizes accurate calculation of updated state, scale matrix, and degree-of-freedom parameters for a coalbed methane near-bit measurement-while-drilling system. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are only some embodiments of the present invention, and those of ordinary skill in the art can also obtain other drawings based on these drawings without creative efforts.

[0042] Figure 1 is a flowchart of a method for establishing a thick-tailed measurement noise filtering model for a near-bit measurement-while-drilling system of the present invention;

[0043] Figure 2 is a comparison curve graph of the noise fluctuations after filtering, the original fluctuations, and the ideal fluctuations of the thick-tailed measurement noise filtering model for the near-bit measurement-while-drilling system of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0044] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the drawings in the embodiments of the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art without creative efforts based on the embodiments of the present invention belong to the scope of protection of the present invention.

[0045] The following further describes the present invention with reference to the embodiments.

[0046] Embodiment 1

[0047] Please refer to the specification appendix Figure 1 , a method for establishing a thick-tailed measurement noise filtering model for a near-bit measurement-while-drilling system, includes the following steps:

[0048] S1: Analyze the influence characteristics of factors such as the impact vibration of the drill string caused by the bit cutting the coal seam on the accelerometer in the near-bit measurement-while-drilling system according to parameters such as the wellbore structure and drill string type during the exploitation process of coalbed methane multi-branch wells. Meanwhile, analyze the interference characteristics of ferromagnetic substances in the drill string and coal seam on the fluxgate in the measurement-while-drilling system.

[0049] Among them, the measurement-while-drilling system is mainly used for real-time monitoring during the construction of near-horizontal directional boreholes in coal mines. It can measure main parameters such as the borehole inclination angle, azimuth angle, and tool face angle of the positive displacement motor while drilling. Meanwhile, it can realize the immediate display of borehole parameters and borehole trajectory, facilitating the drillers to understand the borehole construction situation at any time and timely adjust the tool face direction and process parameters of the positive displacement motor, so that the borehole extends as much as possible along the designed trajectory. The downhole measurement-while-drilling inclinometer usually uses a fluxgate or gyroscope to provide the azimuth angle information of the bit, and cooperates with an accelerometer to measure the gravity field to calculate the well inclination angle and tool face angle. The fluxgate is easily affected by magnetic interference generated by solar storms, drilling fluid, coal seam ferromagnetic minerals, and drill pipes, resulting in large measurement errors.

[0050] S2: Explore the measurement noise-induced measurement outlier characteristics of the accelerometer and fluxgate in the near-bit measurement-while-drilling system under impact vibration and complex magnetic field interference, further explore the heavy-tailed measurement noise characteristics of the near-bit measurement-while-drilling system caused by sensor measurement outliers, and establish a Student's T distribution model under the posterior probability density function.

[0051] Among them, the Student's T distribution model under the posterior probability density function is determined by the continuous measurement of the gravity field and geomagnetic field parameters of the downhole instrument by the gravity accelerometer and fluxgate, on the basis of using the traditional Gaussian approximation state to estimate the sensor measurement noise, and is determined by the Gaussian approximation state estimation, induced measurement outliers, and heavy-tailed measurement noise.

[0052] Among them, the Gaussian approximation state estimation is determined by the following formula:

[0053] x k =f k-1 (x k-1 )+q k-1 ;

[0054] Z k =h k (x k )+e k ;

[0055] In the formula, k represents the discrete time series, 0 ≤ k ≤ M, M is any moment, x k represents the set composed of all state vectors from the 0th moment to the Mth moment, z kDenote the set composed of all measurement vectors at time instants from 1 to M, f k-1 (x k-1 ) and h k (x k ) are arbitrary known functions, q k and e k are the system noise and measurement noise respectively; q k is Gaussian white noise, and e k is colored heavy-tailed noise.

[0056] The colored heavy-tailed noise is determined by the following formula:

[0057] e k = Ψ k-1 e k-1 + ξ k-1 ;

[0058] In the formula, Ψ k-1 is the known correlation parameter. ξ k is white heavy-tailed noise;

[0059] The Student's T distribution model is determined by the following formula:

[0060]

[0061] In the formula, t(ξ k ; O, R, v) represents the Student's t probability density function with mean 0, scale matrix R, and degrees of freedom parameter v, represents the Gaussian probability density function with mean 0 and variance , represents the Gamma probability density function, and λ k is the auxiliary random variable.

[0062] S3: In the near-bit measurement-while-drilling system for coalbed methane multi-branch wells, the noise scale matrix and degrees of freedom parameter in the model after differencing the accelerometer and fluxgate measurements are unknown; establish the conjugate prior distributions of the unknown parameters and the state to be estimated, and use the variational Bayesian method to update the posterior probability density functions of the state, scale matrix, and degrees of freedom parameter to Gaussian, inverse Wishart, and Gamma distributions respectively, and simultaneously estimate the unknown state, scale matrix, and degrees of freedom parameter;

[0063] Among them, the inverse Wishart and Gamma distributions are determined by the following formula:

[0064] Wt(R; u 0 , U 0 );

[0065] The first formula represents the inverse Wishart probability density function. In the formula, u0 represents the degrees of freedom parameter of the inverse Wishart probability density function, U 0 represents the inverse scale matrix of the inverse Wishart probability density function;

[0066]

[0067] The second formula represents the Gamma probability density function.

[0068] Establish the probability density function of the conjugate prior distribution of the unknown parameters and the state to be estimated;

[0069] Among them, the probability density function of the conjugate prior distribution is determined by the following formula:

[0070]

[0071] In the formula, Wt(R; u 0 , U 0 ) represents the inverse Wishart probability density function with degrees of freedom parameter u 0 and inverse scale matrix U 0 ; The initial state x 0 is a Gaussian random vector with mean and covariance matrix and P 0|0 respectively; And the initial state x 0 , the system noise q k , and the measurement noise e k are independent of each other. is a Gaussian probability density function with mean and covariance matrix and P 0|0 respectively; G(v; a 0 , b 0 ) represents the Gamma probability density function with shape parameter a 0 and rate parameter b 0 respectively.

[0072] In order to design Gaussian approximation filters and smoothers with colored heavy-tailed measurement noise, it is necessary to whiten the colored measurement parameters using the measurement difference method;

[0073] The colored measurement parameters are whitened using the measurement difference method through the following formula:

[0074] b k = z k - Ψ k-1 Z k-1 ;

[0075] In the formula, b k is the re-constructed white measurement.

[0076] S4: Combine the state extension method and the variational Bayesian method to find an approximate solution to the joint posterior filtering probability density function;

[0077] Among them, the extended state vector is obtained through the following formula:

[0078] δ k :=[x k x k - 1 T ;

[0079] Among them, δ k is the extended state vector.

[0080] S5: Establish a robust Gaussian approximation filter and a robust Gaussian approximation smoother model with colored thick-tailed measurement noise to achieve accurate calculation of the updated state, scale matrix, and degrees of freedom parameters of the coalbed methane near-bit measurement-while-drilling system.

[0081] Figure 2 This is a comparison curve graph of the noise fluctuations after filtering by the thick-tailed measurement noise filtering model of the near-bit measurement-while-drilling system of the present invention, the original fluctuations, and the ideal fluctuations. It can be seen that, compared with the original root mean square error, the root mean square error after filtering and smoothing by the present invention is closer to the ideal root mean square error.

[0082] The present invention comprehensively analyzes the working state of the coalbed methane directional drilling device, studies the thick-tailed measurement noise characteristics induced by measurement outliers generated by the accelerometer and fluxgate in the near-bit measurement-while-drilling system due to drill string vibration and magnetic field interference, builds a Student's T distribution model of the noise characteristics, and simultaneously estimates the unknown state, scale matrix, and degrees of freedom parameters by using the state extension method and the variational Bayesian method; studies a new robust Gaussian approximation filter and smoother, and establishes a new non-linear measurement noise filtering model for accelerometer and fluxgate measurements to improve the robustness and measurement accuracy of the sensor.

[0083] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements on some of the technical features; and these modifications or replacements will not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.​

Claims

1. Method for establishing thick-tailed measurement noise filtering model of near-bit measurement-while-drilling system Characterized in that It includes the following steps: S1: Analyze the influence characteristics of the drill string impact vibration factors caused by the drill bit cutting the coal seam on the accelerometer in the near-bit measurement-while-drilling system, and at the same time analyze the interference characteristics of ferromagnetic substances in the drill string and the coal seam on the fluxgate in the measurement-while-drilling system; S2: Measure the noise-induced measurement outlier characteristics of the accelerometer and the fluxgate in the near-bit measurement-while-drilling system under impact vibration and complex magnetic field interference, further explore the thick-tailed measurement noise characteristics of the near-bit measurement-while-drilling system caused by sensor measurement outliers, and establish a Student's T distribution model under the posterior probability density function; S3: Establish the probability density function of the conjugate prior distribution of unknown parameters and states to be estimated, and use the variational Bayesian method to update the posterior probability density functions of the state, scale matrix, and degree-of-freedom parameters to Gaussian, inverse Wishart, and Gamma distributions respectively, and at the same time estimate the unknown state, scale matrix, and degree-of-freedom parameters; S4: Combine the state extension method and the variational Bayesian method to find an approximate solution of the joint posterior filtering probability density function; S5: Establish a robust Gaussian approximation filter and a robust Gaussian approximation smoother model with colored thick-tailed measurement noise to achieve accurate calculation of the updated state, scale matrix, and degree-of-freedom parameters of the coalbed methane near-bit measurement-while-drilling system; In step S2, the Student's T distribution model under the posterior probability density function is determined by the Gaussian approximate state estimation, induced measurement outliers, and thick-tailed measurement noise on the basis of continuously measuring the gravity field and geomagnetic field parameters of the downhole instrument by using the gravity accelerometer and the fluxgate; The Gaussian approximation state estimation is determined by the following formula: ; ; where \(k\) represents a discrete-time sequence, and \(M\) is any moment, denotes the set composed of all state vectors from time 0 to time \(M\), denotes the set composed of all measurement vectors from time 1 to time \(M\), and are arbitrary known functions, and are system noise and measurement noise respectively; is Gaussian white noise, is colored heavy-tailed noise.

2. The method for establishing a thick-tailed measurement noise filtering model of the near-bit measurement-while-drilling system according to claim 1 Characterized in that The colored heavy-tailed noise is determined by the following formula: ; wherein, are known related parameters; is white thick-tailed noise.

3. The method for establishing a thick-tailed measurement noise filtering model of the near-bit measurement-while-drilling system according to claim 1 Characterized in that The Student's t-distribution model is determined by the following formula: ; wherein, represents a Student’s t probability density function with a mean of 0, a scale matrix of R, and a degree-of-freedom parameter of , represents a Gaussian probability density function with a mean of 0 and a variance of , represents a Gamma probability density function, is an auxiliary random variable.

4. The method for establishing a thick-tailed measurement noise filtering model of the near-bit measurement-while-drilling system according to claim 1 Characterized in that In step S3, the inverse Wishart and Gamma distributions are determined by the following formulas: Inverse Wishart probability density function: ; wherein, represents the degrees of freedom parameter of the inverse Wishart probability density function, represents the inverse scale matrix of the inverse Wishart probability density function; Gamma probability density function: .

5. The method for establishing a thick-tailed measurement noise filtering model of the near-bit measurement-while-drilling system according to claim 1 Characterized in that The probability density function of the conjugate prior distribution is determined by the following formula: ; wherein, denotes an inverse Wishart probability density function with a degree - of - freedom parameter of and an inverse scale matrix of ; the initial state is a Gaussian random vector with a mean and a covariance matrix being and respectively; and the initial state , the system noise , and the measurement noise are independent of each other; is a Gaussian probability density function with a mean and a covariance matrix being and respectively; denotes a Gamma probability density function with a shape parameter of and a rate parameter of .

6. The method for establishing a thick-tailed measurement noise filtering model of the near-bit measurement-while-drilling system according to claim 1 Characterized in that Step S3 further includes: whitening the colored heavy-tailed measurement parameters by using the measurement difference method, which is carried out through the following formula: ; wherein, is the re-constructed white measurement.

7. The method for establishing a thick-tailed measurement noise filtering model of the near-bit measurement-while-drilling system according to claim 1 Characterized in that In step S4, the extended state vector is obtained through the following formula: ; Among them, is the extended state vector.

8. A thick-tailed measurement noise filtering model of a near-bit measurement-while-drilling system constructed by the establishment method according to any one of claims 1 to 7

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