关键词: 随机抽样一致性, 主成分分析, 列文伯格-马夸尔特算法, 空心圆柱体, 拟合算法

Abstract: This paper addresses the challenge of accurate fitting of a hollow cylinder for concentricity detection of wellhead on a super-large jacket platform， particularly under conditions of sparse and unevenly distributed feature points and weak geometric constraints， which are often prone to significant initial deviation and poor convergence. A robust fitting method integrating random sample consensus（RANSAC）， principal component analysis（PCA）， and Levenberg-Marquardt（LM） algorithms is proposed. The method begins by combining RANSAC and PCA to rapidly estimate the initial axis of the cylinder. The inner and outer wall points are then automatically distinguished based on the bimodal distribution of the distance histogram， eliminating the need for manual labeling. Finally， an adaptive damping LM algorithm is applied to achieve precise nonlinear parameter fitting， ensuring both convergence speed and stability. Simulations and field tests show that the proposed algorithm significantly outperforms conventional methods in terms of axis orientation error， fitting accuracy of inner and outer radii， and the root mean square （RMS） of feature point residuals， demonstrating its effectiveness and practical value in engineering applications.

Key words: random sample consensus, principal component analysis, Levenberg-Marquardt algorithm, hollow cylinders, fitting algorithm