结合地下水环境解逆问题的数值方法及其优化

Numerical solution and optimizing methods for solving inverse problem related to underground water

研究了偏微分方程定解问题的逆问题分类,结合地下水流建立了解逆问题的数学模型,归纳了逆问题的特点,并较全面地分析了逆问题的数值解法。对试估-校正法、高斯牛顿法、数学规化法等作了深入分析,讨论了目前国内外流行的3种全局优化方法:模拟退火法、模拟进化法和神经网络法。对不同方法的优缺点及适用情况作了分析,阐述了各种数值方法的合理性及优越性。研究结果表明,无论是直接方法还是间接方法都各有各的利弊,各有各的使用条件,可具体情况具体分析,选取哪种方法由所求参数个数、观测资料多少、计算机计算时长、优化后结果可靠性等因素来确定。本文分析的数值解法及优化可在类似地下水资源评估和地下水流场计算中推广应用。

The classification of the inverse problem with partial differential equation is studied. The mathematic model of inverse problem related to undergrund water is eslablished. And its characteristics are summerizd. The numberical solution is analyzed. EstimationCorrection, GaussNewton method and Mathematical Projection are analyzed. Three global optimizing methods, stimulating annealing algorithm, simulating evolution, and neural network are studied. Their properties, application and advantages are described. The research results show thatwe should make a concrete analysis to the problems.The reseach method is decided by the number of parameters, the amount of observation material,the calculation time of computer and the optimized result reliability etc. The numberical solution and optimizing method which are analyzed, can be extended to the application of the evaluation of analogous underground water resource and the calculation of underground water flow field.