Abstract: Based on the Newton iteration method， a parameter estimation method of cumulative Logistic regression was proposed. The selection of primary values of iteration， the relationship of sizes of constant coefficients and the singularity of Hessian matrix were analyzed， which are the main problems influencing stypticity in the process of iteration. Through the self-adaptive selection of primary values of iteration and control of the iteration process， the singularity of Hessian matrix was avoided. The data of the bearing database of Case Western Reserve University was used for validation. The experiment results show that the accuracy of model training and verification proposed is higher than that of the statistics software SPSS. Moreover， the robustness of the proposed algorithm is proved by the Booststrap random testing method.

Key words: cumulative Logistic regression, parameter estimation, Hessian matrix, adaptive algorithm, rolling bearing, health state assessment