Application of Machine Learning for Tool Condition Monitoring in Turning

The machining process is primarily used to remove material using cutting tools. Any variation in tool state affects the quality of a finished job and causes disturbances. So, a tool monitoring scheme (TMS) for categorization and supervision of failures has become the utmost priority. To respond, traditional TMS followed by the machine learning (ML) analysis is advocated in this paper. Classification in ML is supervised based learning method wherein the ML algorithm learn from the training data input fed to it and then employ this model to categorize the new datasets for precise prediction of a class and observation. In the current study, investigation on the single point cutting tool is carried out while turning a stainless steel (SS) workpeice on the manual lathe trainer. The vibrations developed during this activity are examined for failure-free and various failure states of a tool. The statistical modeling is then incorporated to trace vital signs from vibration signals. The multiple-binary-rule-based model for categorization is designed using the decision tree. Lastly, various tree-based algorithms are used for the categorization of tool conditions. The Random Forest offered the highest classification accuracy, i.e., 92.6%.

     

给定度序列图的覆盖成本和反向覆盖成本的研究

具有n个顶点且度序列为(m,2,…,2,1,…,1)(1的重数为m)的连通图不止一个(这些图均为树),而每个树对应唯一一个段序列(l₁,l₂,…,l_m).通过对任意一树移动最长段的悬挂点到最短段悬挂点的方式得到另一树,比较前后两树的覆盖成本和反向覆盖成本,给出了具有最小覆盖成本和反向覆盖成本的极树,并且进一步给出了取得最小覆盖成本和反向覆盖成本的顶点.     

Variations of the Catalan numbers from some nonassociative binary operations

We investigate certain nonassociative binary operations that satisfy a four-parameter generalization of the associative law. From this we obtain variations of the ubiquitous Catalan numbers and connections to many interesting combinatorial objects such as binary trees, plane trees, lattice paths, and permutations.     

Surface modification of date palm activated carbonaceous materials for heavy metal removal and CO2 adsorption

In this study, high surface area activated carbon (AC) was prepared from a local palm tree (Phoenix Dactylifera) using a variety of metal carbonates activators and finally achieved an excellent S_BET of 2700 m²/g when Cs₂CO₃ was used as an activating agent at a temperature of 600 °C. Surface modification of AC was carried out using various nitrogen transporting agents, resulting in N-doped ACs with nitrogen content varying from 4.0 to 11.4 %, depending on the functionalizing agents and activators used. The bimodal (presence of micro- as well as meso-porosity) ACs with such excellent surface properties were studied for their CO₂ uptake capacity at two different temperatures (0 and 25 °C) by isotherms recorded at pressure 1 bar and showed a remarkable uptake ability of 3.52 mmol/g (at 25 °C) and 5.6 mmol/g (at 0 °C), respectively. Also, batch experiments with variable pH, contact time, adsorbate concentrations, adsorbent dose, and temperatures were evaluated to understand the mechanism of sorption phenomena of Cr(VI) and Pb(II) achieving > 99.9 % removal capacity by the prepared ACs. Depending on the heavy metal ions being investigated, it was revealed that the pH of the solution and the amount of adsorbent had a direct impact on the total adsorption ability. Nitrogen atoms doped into the carbon frameworks were found to enhance the adsorption in the case of Pb(II) while the removal of Cr(VI) appeared to be unaffected. Maximum adsorption for Cr(VI) was observed at pH 2 and was determined to follow Freundlich isotherm while that of Pb(II) was observed at pH 7 and follows Langmuir isotherm. Best adsorption was found at an adsorbate concentration of 10 ppm and an adsorbent dose of 10 g/L. Kinetic modeling parameters showed the applicability of pseudo-second-order model perfectly.     

Classification of nasopharyngeal cell lines (C666-1, CNE2, NP69) via Raman spectroscopy and decision tree

Researchers have demonstrated that Raman spectroscopy can be used for characterization of tumor cells with excellent spatial resolution. However, performance evaluation of different algorithms in classifying multiclass of Raman spectra has not been reported yet. In this work, we present Raman spectra of nasopharyngeal carcinoma and nasopharyngeal normal cell lines. Combined with student’s t-test and several multivariate approaches, including decision tree, support vector classification, and linear discriminant analysis, our work shows that the relative content of two histological abnormality sensitive bands at 1449 and 1658 cm⁻¹ in tumor cells is significantly different from that of normal cells (p = 0.0132), and can be a biomarker to classify these cells. This difference is confirmed by importance analyses in the decision tree model. Furthermore, performances of statistical methods are compared with one another to explore the ability in classification. Results show that the decision tree can be more capable for classification between tumorous and normal cell lines with sensitivity and specificity of 99.0% and 96.9%, respectively. Findings of this work further support our previous work and indicate that the decision tree performs more robustly in cell classification. Our work will prove helpful to the early diagnosis of nasopharyngeal carcinoma, and will indicate the decision tree to be the primary algorithm in tumor-cell classification.     

Leaf‐Critical and Leaf‐Stable Graphs

The minimum leaf number ml(G) of a connected graph G is defined as the minimum number of leaves of the spanning trees of G if G is not hamiltonian and 1 if G is hamiltonian. We study nonhamiltonian graphs with the property for each or for each . These graphs will be called ‐leaf‐critical and l‐leaf‐stable, respectively. It is far from obvious whether such graphs exist; for example, the existence of 3‐leaf‐critical graphs (that turn out to be the so‐called hypotraceable graphs) was an open problem until 1975. We show that l‐leaf‐stable and l‐leaf‐critical graphs exist for every integer , moreover for n sufficiently large, planar l‐leaf‐stable and l‐leaf‐critical graphs exist on n vertices. We also characterize 2‐fragments of leaf‐critical graphs generalizing a lemma of Thomassen. As an application of some of the leaf‐critical graphs constructed, we settle an open problem of Gargano et al. concerning spanning spiders. We also explore connections with a family of graphs introduced by Grünbaum in correspondence with the problem of finding graphs without concurrent longest paths.     

自由Rota-Baxter代数的因子分解

近年来,Rota-Baxter代数在数学和物理学中有着广泛的应用,受到越来越多的关注,自由Rota-Baxter代数分别用括号字,根树以及Motzkin路径得到了构造.因子分解在代数学中是一个很重要的问题.本文主要考虑用括号字构造的自由RotaBaxter代数,得到了自由Rota-Baxter代数中基元素的因子分解.     

Expression for the Number of Spanning Trees of Line Graphs of Arbitrary Connected Graphs

For any graph G, let be the number of spanning trees of G, be the line graph of G, and for any nonnegative integer r, be the graph obtained from G by replacing each edge e by a path of length connecting the two ends of e. In this article, we obtain an expression for in terms of spanning trees of G by a combinatorial approach. This result generalizes some known results on the relation between and and gives an explicit expression if G is of order and size in which s vertices are of degree 1 and the others are of degree k. Thus we prove a conjecture on for such a graph G.