Parametric inversion method based on interval well-posedness and interval ill-posedness theory
Tang Limin Zheng Jianlong
1. State Engineering Laboratory of Highway Maintenance Technology, Changsha University of Science & Technology， Changsha 410004, China;
2. School of Traffic and Transportation Engineering, Changsha University of Science & Technology, Changsha 410004, China;
3. Co-Innovation Center for Advanced Construction and Maintenance Technology of Modem Transpotation Infrastructural Facility, Changsha 410004, China
Abstract：It is pointed out that there are two kinds of ill-posed problems during the parametric inversion of Duncan-Chang model. According to the properties of objective function of parametric inversion in different intervals and the classical definition of ill-posed problems, the concepts of interval well-posedness and interval ill-posedness for parametric inversion are put forward, and then the definitions of well-posed interval and ill-posed interval are given. Based on the monotonicity of function and the property of function derivative, the method of determining well-posed interval and ill-posed interval for the inversion of one or two parameters is developed. Results show that the parametric inversion based on the interval well-posedness and interval ill-posedness theory can effectively determine the well-posed interval and inversion results for parametric inversion of Duncan Chang model.
