Objectives In order to withstand the deep water pressure, the cylindrical structure and the conical structure are often used as the submarine pressure hull. The section roundness of the submarine pressure hull needs to be measured during construction and repair. Due to the limitation of environment conditions and the fusion of different survey methods to obtain data, the survey points are often non-uniform. This case would result in the deviation between the results of classical least square circle fitting method and the actual situation, especially to the maximum deflection which is used as the judgment condition of roundness. Therefore, it is necessary to adopt a method to eliminate the influence of non-uniform distribution of the survey points.

Methods A non-uniform sampling weighted least squares circle fitting method and its weighting rules are proposed based on the classical Pratt circle fitting method. There are three steps in the proposed method. First, the survey points are fitted by the classical Pratt method. Then, the weight of point is calculated according to the corresponding center angle. Finally, the survey points with weight are fitted.

Results Numerical experiments on standard ellipse sampling analysis are carried out. The results show that the maximum deflection is more affected than the fitted center and radius by the non-uniformity of the sampling points. Because the roundness evaluation judgment of the submarine pressure hull is based on the maximum deflection, the fitting results of the proposed method are more accurate and reliable than the classical circle fitting method.

Conclusions The proposed method can eliminate the influence of non-uniform sampling on circle fitting better, and has good accuracy and engineering practical value.