算子识别反问题模型优化与数据优化的联合反演技术

Associated inversion techniques of model optimization and data optimization for inverse problem of operator identification

针对算子识别反问题,分析了解的不适定性与模型误差、数据误差的关系,建立了基于模型优化和数据优化的联合反演技术,提出了适合同时处理数字式数据与非数字式数据的量化单调消噪方法。建立了数值反演可靠性概念,包括正演算子可靠性、正演计算可靠性、测量设计可靠性、反演算法可靠性、反演计算可靠性、测量数据可靠性,并建立了相应的可靠性定量评估方法。通过一个岩土工程的算子识别反问题的工程应用与数值试验说明:其一,这一联合反演技术实质是一门系统性的优化技术,能够显著提高数值反演的可靠性和准确度;其二,应用可靠性定量评估方法,能够客观地、定量地获得反问题解估计的质量评定。

The paper analyses the relationship between model errors, data errors and illposedness of solutions for inverse problems of operator identification,establishes associated inversion techniques based on model optimization and data optimization,proposes monotonic denoise method of quantization data, which can deal with both digital data and nondigital data and establishes reliability concepts of numerical inversion, including reliability of direct operator, reliability of direct calculation, reliability of measurement design, reliability of inverse algorithm, reliability of inverse calculation, reliability of measuring data, and proposes their corresponding quantitative evaluation methods for numerical inversion reliability. By a numerical experiment of operator identification problem in geotechnical engineering, two conclusions are obtained: first, the associated inversion technique is a systematic optimization technique, and can increase reliability and degree of accuracy of numerical inversion obviously; second, through applying reliability evaluating methods of numerical inversion, the quality evaluation of solution estimation of inverse problem can be achieved objectively and quantitatively.