There are two types of inverse problems: Optimization designation and parameter identification. Before the parameter identification of mathematical and physical inverse problems, it is necessary to determine the numbe...There are two types of inverse problems: Optimization designation and parameter identification. Before the parameter identification of mathematical and physical inverse problems, it is necessary to determine the number and position of measurement points in analysis and evaluation of a large number of measured data. In this paper, a mathematical methodology is proposed to describe the influence of the number and position of measurement points on the reconstruction precision. Information entropy and Bayesian theory are used in the description. Finally, a numerical experiment shows that the methodology is effective.展开更多
基金the National Natural Science Foundation of China (Grant Nos. 60531010 and 60471045)
文摘There are two types of inverse problems: Optimization designation and parameter identification. Before the parameter identification of mathematical and physical inverse problems, it is necessary to determine the number and position of measurement points in analysis and evaluation of a large number of measured data. In this paper, a mathematical methodology is proposed to describe the influence of the number and position of measurement points on the reconstruction precision. Information entropy and Bayesian theory are used in the description. Finally, a numerical experiment shows that the methodology is effective.
