Abstract
Reconstruction methods for discrete data, such as the Moving Least Squares (MLS) and Moving Total Least Squares (MTLS), have made a great many achievements with the progress of modern industrial technology. Although the MLS and MTLS have good approximation accuracy, neither of these two approaches are robust model reconstruction methods and the outliers in the data cannot be processed effectively as the construction principle results in distorted local approximation. This paper proposes an improved method that is called the Moving Total Least Trimmed Squares (MTLTS) to achieve more accurate and robust estimations. By applying the Total Least Trimmed Squares (TLTS) method to the orthogonal construction way in the proposed MTLTS, the outliers as well as the random errors of all variables that exist in the measurement data can be effectively suppressed. The results of the numerical simulation and measurement experiment show that the proposed algorithm is superior to the MTLS and MLS method from the perspective of robustness and accuracy.
Highlights
Nowadays, benefitting from the development of reverse engineering and computer technology, the meshless method widely used for reconstructing the discrete data has been studied by varieties of scholars, and different types of meshless methods have been proposed [1,2]
To suppress the influence of outliers, we propose an improved reconstruction algorithm called the Moving Total Least Trimmed Squares (MTLTS) method for accurate curve and surface profile analysis, in which the TLTS method using Singular Value Decomposition (SVD) [33] is employed to deal with the abnormal data in the influence domain
The remainder of the paper is structured as follows: in the Section 2, a description of the Moving Total Least Squares (MTLS) and Moving Least Squares (MLS) method is drawn briefly; the Section 3 introduces the principle of the MTLTS method; in the Section 4, we give the results of numerical simulation and measurement experiment and make a brief analysis; lastly, we show the conclusions in the Section 5
Summary
Centre for Precision Technologies, University of Huddersfield, Huddersfield HD1 3DH, UK; CAS Key Laboratory of Mechanical Behaviour and Design of Materials, Department of Modern Mechanics, University of Science and Technology of China, Hefei 230022, China Received: 10 October 2020; Accepted: 6 November 2020; Published: 12 November 2020
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