Method of separation for characterized curve errors of helicoidal surfaces based on dynamic GM(1,1) and least-squares

For evaluating the characterized curve errors of helicoidal surfaces, it is very important to separate the errors into form errors and angle errors. The existence of abnormal data reduces the quality of the measurement data to a great extent, and results in inaccurate separation results for the characterized curve errors. Hence how to detect and remove abnormal data is very critical for evaluating the characterized curve errors. The common characteristic of the existing methods for detecting abnormal data is that they strongly depend on the prior knowledge and sample size of the primary measurement data, and need large amounts of calculation. Unfortunately it is difficult to get large sample sizes in some measurements. The existing methods are therefore limited in applications. Based on the dynamic GM(1,1), this paper presents a novel effective method for detecting abnormal data. The model by implementing the dynamic GM( 1,1) for the primary measurement data can be a good approximation to normal data, while insensitive to abnormal data. Through comparing the model with the primary measurement data, abnormal data can be effectively detected. Then the least-squares method is used to separate the characterized errors into form errors and angle errors.