Inversion and Error Analysis of Target Material Proportion from Scattering Spectrum

In this work, we have proposed a scattering spectra-based method for inverting the surface materials and material proportions of space objects (SOs) from long distances. The results of this work shall improve efforts to characterize and predict the orbits of space debris. We first constructed a physical model for SO characterization based on scattering spectra and then provided a least-squares solution with minimum-norm (LSMN) algorithm for inverting the surface materials and material proportions of an SO. The optical reflectance of complex material surfaces was characterized using a bidirectional reflectance distribution function (BRDF)-based multimodal fusion model that uses the characteristics of the light source, the reflectance of the target’s surface materials, and structures, and the angle of incidence and reflection. The area of each material in the BRDF was then treated as the to-be-inverted parameter. The proposed method was then experimentally validated using four sets of materials. The materials and proportions of equiproportional and non-equiproportional combinations of materials were inverted by the proposed method, and the average inversion error was less than 10%. According to the relationship curve be-tween experimental data error and inversion error, and between theoretical error and inversion error, it can be concluded that the accuracy of inversion error has a linear relationship with the measurement data error. In summary, we have provided a new technical approach for the inversion and characterization of SO materials and material proportions from long distances.

MODEL OF CEMENT RAW MATERIAL PROPORTION AND ITS SOLUTION

Cement is a kind of colloid material. This paper introduces a model of raw material proportion and quadratic programming for solving the model when three kinds of raw materials are mixed. The calculation of the raw material proportion is easy, and its result is reliable. This model is apt to be realized on micro-computer. This paper indicates the defects of the least square method and compares these two methods through existing instance.

PROPORTION OF THE CEMENT RAW MATERIAL CALCULATED BY THE LINEAR PROGRAMING

This paper presents a new method .linear programming method. to calculate the proportion of the cement raw material. Its advanlages are as following : good practicability, convenience for analysis, and being easy for controlling. The mathematical model given in the paper is apt to be realized on computer.