The way of measuring diameter by use of measuring bow height and chord length is commonly adopted for the large diameter work piece. In the process of computing the diameter of large work piece, measurement uncertainty is an important parameter and is always employed to evaluate the reliability of the measurement results. Therefore, it is essential to present reliable methods to evaluate the measurement uncertainty, especially in precise measurement. Because of the limitations of low convergence and unstable results of the Monte-Carlo (MC) method, the quasi-Monte-Carlo (QMC) method is used to estimate the measurement uncertainty. The QMC method is an improvement of the ordinary MC method which employs highly uniform quasi random numbers to replace MC's pseudo random numbers. In the process of evaluation, first, more homogeneous random numbers (quasi random numbers) are generated based on Halton's sequence. Then these random numbers are transformed into the desired distribution random numbers. The desired distribution random numbers are used to simulate the measurement errors. By computing the simulation results, measurement uncertainty can be obtained. An experiment of cylinder diameter measurement and its uncertainty evaluation are given. In the experiment, the guide to the expression of uncertainty in measurement method, MC method, and QMC method are validated. The result shows that the QMC method has a higher convergence rate and more stable evaluation results than that of the MC method. Therefore, the QMC method can be applied effectively to evaluate the measurement uncertainty.
Because measurement uncertainty is an important parameter to evaluate the reliability of measurement results, it is
essential to present reliable methods to evaluate the measurement uncertainty especially in precise optical measurement.
Though Monte-Carlo (MC) method has been applied to estimate the measurement uncertainty in recent years, this
method, however, has some shortcomings such as low convergence and unstable results. Therefore its application is
limited. To evaluate the measurement uncertainty in a fast and robust way, Quasi Monte-Carlo (QMC) method is adopted
in this paper. In the estimating process, more homogeneous random numbers (quasi random numbers) are generated
based on Halton's sequence, and then these random numbers are transformed into the desired distribution random
numbers. An experiment of cylinder measurement is given. The results show that the Quasi Monte-Carlo method has
higher convergence rate and more stable evaluation results than that of Monte-Carlo method. Therefore, the quasi
Monte-Carlo method can be applied efficiently to evaluate the measurement uncertainty.
Shape Distribution is fast, simple, and robust method in 3D model retrieve. This method, however, only considers
distances between the objects' shape distribution histograms and ignores the information included. As the result, the
retrieval precision is low. To enhance the retrieve efficiency, a novel method which integrates Shape Distribution and
Self-Organizing Feature Map (SOFM) is proposed. The models' shape distribution histograms are established by Shape
Distribution and transformed into the proper format of SOFM. The similar models are grouped in neighboring neurons of
SOFM by using competitive learning approach. In addition, the dissimilar models are indexed in far away neurons. With
the given query model, SOFM classifies it into the proper cluster and exports the retrieval results. A case study is
presented and the results show that the retrieval precision of the proposed method is higher than that of the Shape
Distribution method.
Owing to its fast speed, simple operation, and strong robustness, Shape Distribution is widely used in search engines.
This method, however, only considers distances between the objects' shape distribution histograms and ignores the
information included. Actually the information of the shape distribution histograms, such as the mean value, the standard
deviation, the kurtosis and the skewness, can be used to map the 3D model. As a result, the retrieval precision of Shape
Distribution is low. To enhance the retrieve efficiency, a novel method which employs the K-means clustering method is
proposed in this paper. First, the models' shape distribution histograms are established by Shape Distribution method and
are normalized as the proper format of K-means clustering method. Then, the objects' shape distribution histograms are
served as inputs of K-means clustering method and are classified into certain groups by this algorithm. Last, all the
models that belong to the classification of the query model are exported as the retrieval results. A case study is used to
validate the proposed method. Experimental results show that the retrieval precision by using the proposed method is
higher than that of the Shape Distribution method.
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