The steps and key points of Li-Yorke algorithm are explained systematically in computing single zero point of a mapping. In the meantime, the brief introduction of the calculation for stress and displacement in the ELS of axial symmetry is provided.The basic theory of homotopy method and the mathematical knowledge about manifold are mainly introduced in chapter 3, and the realization with the continuous homotopy method discussed. The major contents and the significance of theory and practice are briefly explained.Chapter 2 presents the mathematical models for the backcalculation of moduli and analyzes the limitations in the current methods. A brief review is given to the research condition and the development history of these problems both at home and abroad. The main contents for each one are as follows:The key problems in Chapter 1 are the ones to be solved in the dissertation. Not only can the trained networks be used in the engineering design and testing, but also in the conventional science and technology research.There are 8 chapters in the dissertation. The results show that the approximate method with homotopy Back-Propagation （BP） neural network is great in precision, fast in speed, wide in range, strong in robustness and easy in realization to calculate the theoretical coefficients of deflection and those of the maximum tensile stress for ELS. The homotopy method can be widely used in the backcalculation analysis of the deflection basins measured with Falling Weight Deflectometer （FWD）.In addition, the approximate calculation for Elastic Layered System （ELS） to be based on the homotopy neural network theory is discussed with the combination of major contents in the dissertation and the current development trend of ANN theory. Therefore, the homotopy method is the backcalculation one with good accuracy, stable results, great efficiency and wide convergency. The evaluation method for load transfer at joints in Portland Cement Concrete （PCC） pavement and the temperature adjustment method for asphalt moduli in Asphalt Concrete （AC） pavement built with the backcalculated results are for the reference in the engineering application. The engineering application analysis shows that the backcalculated results with the homotopy method present the strength, stiffness and performance of pavement in a better way. A lot of analysis, validation and comparison show that the homotopy method has not only solved efficiently problems of the initial value, partial convergency, poor stability in mathematical progranlnling methods, but also overcome shortcomings of the slow speed for GA and the poor accuracy of ANN. Abstract： The backcalculation of pavement layer moduli is discussed in this dissertation with the homotopy method, and the modified Genetic Algorithm （GA） and the Artificial Neural Network （ANN） also discussed for the comparative analysis.
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