On-line compensation for geomagnetic error while drilling based on magnetic inertial slime mould algorithm

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.