引用本文: 王乐洋, 许冉冉, 靳锡波, 丁锐. 非线性反演算法的综合评价对比[J]. 武汉大学学报 ( 信息科学版), 2022, 47(3): 341-351.
WANG Leyang, XU Ranran, JIN Xibo, DING Rui. Comprehensive Evaluation and Comparison of Nonlinear Inversion Algorithms[J]. Geomatics and Information Science of Wuhan University, 2022, 47(3): 341-351.
 Citation: WANG Leyang, XU Ranran, JIN Xibo, DING Rui. Comprehensive Evaluation and Comparison of Nonlinear Inversion Algorithms[J]. Geomatics and Information Science of Wuhan University, 2022, 47(3): 341-351.

## Comprehensive Evaluation and Comparison of Nonlinear Inversion Algorithms

• 摘要: 结合蒙特卡罗方法的精度评定特点，提出了一种将偏差和中误差作为评价指标的综合评价公式。利用所提出的综合评价公式评价神经网络算法（neural network algorithm，NNA）、基因遗传算法（genetic algorithm，GA）和模拟退火算法(simulated annealing, SA)在火山复式位错模型(compound dislocation model, CDM)和地震Okada模型反演中的精度信息。实验结果表明，无论是基于CDM模型还是基于Okada模型，以上3种方法的参数估值差距较小，但不同方法的精度差别较大。使用所提方法对NNA、GA和SA进行精度计算，结果发现：在火山CDM模型中，采用GA和SA计算所得部分参数中误差较大，且GA和SA综合评价值3.982 0和11.398 8均大于NNA综合评价值3.613 1。在Okada模型中，模拟退火算法所得中误差相对基因遗传算法和神经网络算法较高，且在芦山地震中，SA的综合评价值11.656 2远远大于NNA和GA的综合评价值3.625 4和4.060 4。由实验结果可知，采用所提方法进行评定，NNA的精度信息较高，结果更具有说服性，GA次之，SA精度较低。

Abstract:
Objectives  As nonlinear models become more complex and data sources become more abundant, people have higher and higher requirements for nonlinear methods and precision.However, the existing research mainly considered the precision evaluation of the algorithm, and ignored how to comprehensively evaluate the applicability of the algorithm based on precision information obtained by calculation.
Methods  Considering the above problems, we propose a method to evaluate the advantages of algorithms based on precision information—non-linear comprehensive evaluation method. The method firstly evaluates the accuracy by the traditional Monte Carlo (MC) method, and uses the calculated deviation and the median error as the evaluation index, and calculates the comprehensive evaluation value according to the proposed comprehensive evaluation formula. We use the proposed method to evaluate the precision information of simulated annealing algorithm (SA), genetic algorithm (GA) and neural network algorithm (NNA) in volcano compound dislocation model (CDM) and seismic Okada model inversion.
Results  The experimental results show that whether it is based on the CDM model or the Okada model, the parameter estimation gap between the above three methods is small, but the precision of the different methods varies greatly. The MC is used to calculate the precision of SA, GA and NNA. It is found that in the volcano CDM, mean square errors in some parameters calculated by SA and GA are relatively large, and the comprehensive evaluation values 11.398 8 and 3.982 0 of SA and GA are larger than the comprehensive evaluation value 3.613 1 of NNA. In the Okada model, the SA has a higher mean square error than GA and NNA, and in the Lushan earthquake, the comprehensive evaluation value of the SA is 11.656 2, which is much larger than the comprehensive evaluation values 4.060 4 and 3.625 4 of the GA and NNA.
Conclusions  The precision information of the NNA is higher when the proposed method is used for evaluation, and the result is more convincing, followed by GA, and SA has lower precision.

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