基于Lebenberg_Marquardt的声发射源定位算法

Sound Source Localization Algorithm Based on Levenberg_Marquardt

摘要: 声发射是一种寻找材料破裂点或地震发声源位置非常有效的方法，在本次实验中介绍了声发射源定位中时差定位法的基本原理，将定位问题转化为多元非线性方程组求解问题。根据问题特点，将传统的Geiger定位算法与Lebenberg_Marquardt算法相结合，通过改进Geiger算法的迭代方向与迭代步，极大地减少了算法的时间复杂度，提高了算法的精确度。数值仿真算例表明：该方法能有效地解决了迭代时雅可比矩阵与其转置矩阵接近奇异时d_k过大的问题，保证了算法的收敛性并且提高了迭代算法的收敛速度。

Abstract: Acoustic emission is an extremely effective method for locating material fracture points or seismic sound sources. In this experiment, the basic principle of time difference localization in acoustic emission source localization is introduced, which transforms the localization problem into a multi-dimensional nonlinear equation solving problem. Based on the characteristics of the problem, the traditional Geiger localization algorithm is combined with the Levenberg_Marquardt algorithm by improving the iteration direction and step of the Geiger algorithm, greatly reducing the time complexity of the algorithm and improving its accuracy. Numerical simulation examples demonstrate that this method effectively solves the problem of excessive d_k when the Jacobian matrix and its transpose matrix are close to singular during iteration, ensuring the convergence of the algorithm and improving the convergence speed of the iterative algorithm.