Digitalized Accurate Modeling of SPCB with Multi-spiral Surface Based on CPC Algorithm

The main methods of the existing multi-spiral surface geometry modeling include spatial analytic geometry algorithms, graphical method, interpolation and approximation algorithms. However, there are some shortcomings in these modeling methods, such as large amount of calculation, complex process, visible errors, and so on. The above methods have, to some extent, restricted the design and manufacture of the premium and high-precision products with spiral surface considerably. This paper introduces the concepts of the spatially parallel coupling with multi-spiral surface and spatially parallel coupling body. The typical geometry and topological features of each spiral surface forming the multi-spiral surface body are determined, by using the extraction principle of datum point cluster, the algorithm of coupling point cluster by removing singular point, and the ＂spatially parallel coupling＂ principle based on the non-uniform B-spline for each spiral surface. The orientation and quantitative relationships of datum point cluster and coupling point cluster in Euclidean space are determined accurately and in digital description and expression, coupling coalescence of the surfaces with multi-coupling point clusters under the Pro/E environment. The digitally accurate modeling of spatially parallel coupling body with multi-spiral surface is realized. The smooth and fairing processing is done to the three-blade end-milling cutter＇s end section area by applying the principle of spatially parallel coupling with multi-spiral surface, and the alternative entity model is processed in the four axis machining center after the end mill is disposed. And the algorithm is verified and then applied effectively to the transition area among the multi-spiral surface. The proposed model and algorithms may be used in design and manufacture of the multi-spiral surface body products, as well as in solving essentially the problems of considerable modeling errors in computer graphics and engineering in multi-spiral surface＇s connection available with approximate methods or graphical methods.

FATOC:Bug Isolation Based Multi-Fault Localization by Using OPTICS Clustering

Bug isolation is a popular approach for multi-fault localization(MFL),where all failed test cases are clustered into several groups,and then the failed test cases in each group combined with all passed test cases are used to localize only a single fault.However,existing clustering algorithms cannot always obtain completely correct clustering results,which is a potential threat for bug isolation based MFL approaches.To address this issue,we first analyze the influence of the accuracy of the clustering on the performance of MFL,and the results of a controlled study indicate that using the clustering algorithm with the highest accuracy can achieve the best performance of MFL.Moreover,previous studies on clustering algorithms also show that the elements in a higher density cluster have a higher similarity.Based on the above motivation,we propose a novel approach FATOC(One-Fault-at-a-Time via OPTICS Clustering).In particular,FATOC first leverages the OPTICS(Ordering Points to Identify the Clustering Structure)clustering algorithm to group failed test cases,and then identifies a cluster with the highest density.OPTICS clustering is a density-based clustering algorithm,which can reduce the misgrouping and calculate a density value for each cluster.Such a density value of each cluster is helpful for finding a cluster with the highest clustering effectiveness.FATOC then combines the failed test cases in this cluster with all passed test cases to localize a single-fault through the traditional spectrum-based fault localization(SBFL)formula.After this fault is localized and fixed,FATOC will use the same method to localize the next single-fault,until all the test cases are passed.Our evaluation results show that FATOC can significantly outperform the traditional SBFL technique and a state-of-the-art MFL approach MSeer on 804 multi-faulty versions from nine real-world programs.Specifically,FATOC’s performance is 10.32%higher than that of traditional SBFL when using Ochiai formula in terms of metric A-EXAM.Besides,the results also indicate that,when checking 1%,3%and 5%statements of all subject programs,FATOC can locate 36.91%,48.50%and 66.93%of all faults respectively,which is also better than the traditional SBFL and the MFL approach MSeer.