Abstract
Due to the influence of the errors of time difference of arrivals (TDOA) and the premeasured velocity in the propagation medium, the existing methods always hold the low location accuracy and efficiency. To increase the location accuracy, the joint inversion of AE/MS sources and propagation velocity is proposed using the full measurements and residual estimation. First, the control equation of the unknown wave velocity is constructed using sensor coordinates and full TDOA measurements, and it is linearized by introducing the additive variables. Second, considering the influence of TDOA errors, the residuals of the TDOA equations are calculated to obtain weights. Finally, the orthogonal projection is applied to separate the additive variables and solve the weighted linear equations for source coordinates. The pencil–lead breaks experiments are carried out to verify the effectiveness and accuracy of the proposed method. The results show that the novel method holds better accuracy and wave velocity inversion than the pre-existing methods. The average positioning error of the novel method is only 3.49 mm, while the errors of the traditional methods are 4.62 mm, 5.08 mm, 6.57 mm, and 11.93 mm, respectively. The positioning performance of the proposed method under different TDOA errors is further proved by simulation tests. The simulation results demonstrate that the positioning performance of the proposed method is better than that of the existing methods under different errors. Moreover, the blast vibration experiment validates that the proposed method holds the location accuracy of 16.65 m, which presents good prospects in engineering applications.
Highlights
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No prior measurement of wave speeds and selection of reference sensors reduce the effect of velocity and arrival errors.
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Analytical solution being given by linearizing the control equation, complex computations and local convergence are circumvented.
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Estimating the noise term in the arrival time difference, the tolerance to TDOA errors is improved.
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Redundant time-difference-of-arrival measurements are fully used to provide new constraints.
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Blasting experiments reveal that positioning accuracy of the method is 72% more accurate than the traditional method.
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The data used to support the fndings of this study are available from the corresponding author upon request.
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Acknowledgements
The research leading to these results received funding from the National Key Research and Development Program (Fund for Young Scientists) under Grant Agreement No. 2021YFC2900400, National Natural Science Foundation of China under Grant Agreement No. 52104077.
Funding
The research leading to these results received funding from the National Key Research and Development Program (Fund for Young Scientists) under Grant Agreement No. 2021YFC2900400, National Natural Science Foundation of China under Grant Agreement No. 52104077.
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All authors contributed to the study conception and design. Material preparation was performed by Jie Chen and Yuanyuan Pu. Data collection and analysis were performed by Jiongkun Chen and Yichao Rui. The first draft of the manuscript was written by Jiongkun Chen, and all authors reviewed and edited on previous versions of the manuscript. All authors read and approved the final manuscript.
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Chen, J., Chen, J., Rui, Y. et al. Joint Inversion of AE/MS Sources and Velocity with Full Measurements and Residual Estimation. Rock Mech Rock Eng (2024). https://doi.org/10.1007/s00603-024-03917-3
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DOI: https://doi.org/10.1007/s00603-024-03917-3