Coal Geology & Exploration


In response to the serious distortion of the azimuth angle of the drilling tool caused by the large measurement error of strap-down micro-electro-mechanical-system (MEMS) magnetometer on the drilling tool in the measurement-while-drilling (MWD) environment, an online compensation method for the geomagnetic error of the drilling tool based on the magnetic-inertial slime mould algorithm (MISMA) was proposed. Firstly, the geomagnetic measurement error compensation model of the drilling tool was established through the analysis on the output error of the magnetometer, and the magnetometer error parameters were sorted into solution vectors. Then, the objective function of the ideal magnetic output data, the radial and tangential Pearson inequality of the drilling tool and the constraint condition of the magnetic field modulus were given based on the slime mould algorithm (SMA) according to the output characteristics of the magnetic-inertial sensor in the MWDhe gyroscope data, and the objective function was taken as the fitness function. In addition, the bounded global search range of the adaptive parameter control algorithm was designed with the ratio of the absolute value of the difference to the sum of the absolute values of the fitness value and the best fitness value of the solution vector of current error parameter to improve the MISMA search ability and convergence speed. Adaptively adjusting the random step (RS) by designing the Geomagnetic Modulus Ratio (GMR) could solve the problem that the SMA is prone to fall into local optimum. Moreover, the fitness value corresponding to the solution vector and the optimal solution vector of current geomagnetic error parameter was calculated and subjected to normalization processing and difference calculation successively. Meanwhile, the in-depth development threshold of the geomagnetic error parameter solution was obtained by combining the adaptive parameter values, and thus the quality of the vector solution of geomagnetic error parameters was further improved. Finally, the error compensation of the magnetometer was carried out to improve the azimuth angle accuracy of the drilling tool. Through simulation experiment and real drilling experiments, it is shown that: MISMA has smaller fitness value and faster decline speed compared with SMA under the same number of iterations. The convergence speed is increased by 37.99%, and the average absolute error of the azimuth angle of the drilling tool can be maintained within 2.37°. Generally, the research could improve the measurement accuracy of strap-down MEMS magnetometer on the drilling tool in coal mine, and it is an effective method to obtain the reliable azimuth angle of drilling tool.


mic-electro-mechanical-system (MEMS), magnetometer, slime mould algorithm (SMA), Geomagnetic Modulus Ratio (GMR), error compensation, azimuth angle, MWD




[1] LUO Tao,YANG Hai,LIANG Haibo,et al. Research on the calibration method of MWD under the cooperation of multiple models[J]. IEEE Sensors Journal,2021,21(1):620−632.

[2] SITARAMGUPTA V V S N,SAKORIKAR T,PANDYA H J. An MEMS–based force sensor:Packaging and proprioceptive force recognition through vibro–haptic feedback for catheters[J]. IEEE Transactions on Instrumentation and Measurement,2022,71:4001911.

[3] NING Zhiwen,FU Jun,CHANG Yang,et al. Improved MEMS magnetometer adaptive filter noise reduction and compensation method[J]. IEEE Sensors Journal,2022,22(2):1252−1264.

[4] ZHANG Xiaojun,MAO Zekun,MA Yumeng,et al. Attitude magnetic measurement compensation method of fiber–optic submarine seismometer[J]. IEEE Sensors Journal,2022,22(13):13023−13029.

[5] LIU Jianguo,LI Xiangang,YAN Shenggang,et al. A novel linear calibration model for three–axis fluxgate magnetometer[J]. IEEE Sensors Journal,2021,21(21):23917−23925.

[6] CHAFI M R S,NARM H G,KALAT A A. Calibration of fluxgate sensor using least square method and particle swarm optimization algorithm[J]. Journal of Magnetism and Magnetic Materials,2023,570:170364.

[7] LIU Feng,WU Jiaqi,QUAN Wei. A genetic algorithm and backpropagation neural network based temperature compensation method of spin–exchange relaxation–free co–magnetometer[J]. Review of Scientific Instruments,2022,93(1):015102.

[8] LI Siran,MA Danyue,LU Jixi,et al. In situ calibration of triaxial coils of a vector optically pumped magnetometers based on a particle swarm optimization algorithm[J]. Measurement,2022,202:111878.

[9] CHEN Zhuo,WANG Zhenxiong,ZHANG Qi,et al. Dynamic compensation of a fluxgate magnetometer based on a hybrid optimizing algorithm[J]. Applied Sciences,2023,13(5):2830.

[10] LI Shimin,CHEN Huiling,WANG Mingjing,et al. Slime mould algorithm:A new method for stochastic optimization[J]. Future Generation Computer Systems,2020,111:300−323.

[11] KABOLI S H A,ALQALLAF A K. Solving non–convex economic load dispatch problem via artificial cooperative search algorithm[J]. Expert Systems with Applications,2019,128:14−27.

[12] WU Shubiao,HEIDARI A A,ZHANG Siyang,et al. Gaussian bare–bone slime mould algorithm:Performance optimization and case studies on truss structures[J]. Artificial Intelligence Review,2023,56:9051−9087.

[13] 杨金显,杨闯,蒋志涛,等. 磁/惯性组合的钻具重力信息自适应提取[J]. 煤炭学报,2017,42(12):3331−3337.

YANG Jinxian,YANG Chuang,JIANG Zhitao,et al. Adaptive extraction of gravity information for drilling tool with magnetic and inertial integrated system[J]. Journal of China Coal Society,2017,42(12):3331−3337.

[14] SHI Lingfeng,LIU Yuyu. Three−step autonomous calibration method for low–cost MEMS inertial/magnetic sensors[J]. IEEE Transactions on Magnetics,2022,58(5):4002112.

[15] LI Supeng,CHENG Defu,WANG Yi,et al. Calibration of strapdown magnetic vector measurement systems based on a plane compression method[J]. Measurement Science and Technology,2023,34(5):055115.

[16] LIU Zongwei,LEI Kan,SONG Jiancheng,et al. A designed calibration approach for the measurement−while−drilling instrument[J]. Applied Sciences,2023,13:61.

[17] DONG Xiaofen,CHEN Guoguang,TIAN Xiaoli,et al. Real–time estimation of roll angles by magnetometer based on two–step adaptive Kalman filter[J]. Measurement,2022,198:111349.

[18] 王坚,梁建,韩厚增. 低成本IMU的多位置旋转现场标定方法[J]. 中国惯性技术学报,2017,25(3):294−298.

WANG Jian,LIANG Jian,HAN Houzeng. Method for low–cost IMU in−field calibration through multi–position rotation[J]. Journal of Chinese Inertial Technology,2017,25(3):294−298.

[19] PIOTROWSKI A P,NAPIORKOWSKI J J,PIOTROWSKA A E. Particle swarm optimization or differential evolution:A comparison[J]. Engineering Applications of Artificial Intelligence,2023,121:106008.

[20] YANG Jinxian,CHAO Lijun. A novel orientation recursive algorithm aiming at catastrophe signals in MWD[J]. IEEE Transactions on Industrial Electronics,2020,67(11):9683−9692.



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