Investigating computational geometry for failure prognostics

Prognostics and Health Management (PHM) is a multidisciplinary field aiming at maintaining physical systems in their optimal functioning conditions. The system under study is assumed to be monitored by sensors from which are obtained measurements reflecting the system’s health state. A health indicator (HI) is estimated to feed a data-driven PHM solution developed to predict the remaining useful life (RUL). In this paper, the values taken by an HI are assumed imprecise (IHI). An IHI is interpreted as a planar figure called polygon and a case-based reasoning (CBR) approach is adapted to estimate the RUL. This adaptation makes use of computational geometry tools in order to estimate the nearest cases to a given testing instance. The proposed algorithm called RULCLIPPER is assessed and compared on datasets generated by the NASA’s turbofan simulator (C-MAPSS) including the four turbofan testing datasets and the two testing datasets of the PHM’08 data challenge. These datasets represent 1360 testing instances and cover different realistic and difficult cases considering operating conditions and fault modes with unknown characteristics. The problem of feature selection, health indicator estimation, RUL fusion and ensembles are also tackled. The proposed algorithm is shown to be efficient with few parameter tuning on all datasets.

Pengaruh pendekatan rigorous mathematical thinking (RMT) terhadap kemampuan berpikir kreatif siswa kelas VII

Salah satu tujuan pendidikan matematika adalah menjadikan siswa berpikir kreatif. Hasil dari berpikir kreatif disebut kreatifitas. Namun pada kenyataanya kreatifitas ini kurang diperhatikan oleh guru dalam pembelajaran. Sehingga kemampuan berpikir kreatif perlu dikembangkan lagi. Pemberian stimulus adalah salah satu cara untuk mengembangkan kemampuan berpikir kreatif. Geometri adalah salah satu bidang dalam matematika. Geometri pada tingkat menengah salah satunya mempelajari tentang bangun datar segiempat dan segitiga. Materi geometri merupakan materi yang sulit dipahami oleh siswa karena sulitnya siswa menangkap konsep dari materi tersebut. Rigorous mathematical Thinking (RMT) merupakan pendekatan pembelajaran yang memiliki tiga unsur penting yang mendorong siswa lebih memahami konsep suatu materi. Dengan pahamnya siswa akan konsep suatu materi maka kemampuan berpikir kreatif siswa akan lebih baik. Hal ini karena dalam berpikir kreatif diperlukan berbagai konsep untuk menyelesaikan masalah matematika. Untuk itu penelitian ini bertujuan untuk mengetahui pengaruh pendekatan RMT terhadap kemampuan berpikir kreatif siswa. Metode penelitian yang digunakan adalah true experimental dan desain penelitian yang digunakan adalah posttest only control design. Hasil dari penelitian menunjukkan bahwa terdapat pengaruh pendekatan RMT terhadap berpikir kreatif siswa bahkah pengaruh tersebut lebih baik dari pendekatan pembelajaran yang biasanya digunakan oleh guru. Namun kriteria lebih baik tidak merujuk pada keseluruhan indikator, hanya satu dua kriteria saja. Abstract One of the purposes of mathematics education is to make students think creatively. The result of creative thinking is creativity. But in fact this creativity is less concerned by teachers in learning. So the creative thinking skills need to be developed again. Stimulus is one of the ways to develop creative thinking skills. Geometry is one of the fields in mathematics. The geometry of the middle level one of them learns about the rectangular and triangular planar figure. Geometry material is material that is difficult for students to understand because it is difficult for students to grasp the concept of the material. Rigorous mathematical Thinking (RMT) is a learning approach that has three important elements that encourage students to better understand the concept of a material. With the student's reward for the concept of material, the student’s creative thinking skills will be better. This is because in creative thinking it takes various concepts to solve the mathematical problems. This research aims to determine the influence of RMT's approach to the creative thinking skills of students. The research method used was true experimental and the research design used was posttest only control design. The results of research show that there is an influence on the RMT approach to creative thinking students are better than the learning approach that teachers typically use. But the better criterion does not refer to the overall indicator, just one two criterion.

Discrete version of the Pythagorean theorem

The following observations are motivated by the facts that the area of a planar figure displayed on a screen can be expressed by a certain number of pixels; and if the figure is drawn by a plotter, then its area can be characterised by the total length of a line which fills it in.The generalisations of the Pythagorean theorem are of three kinds. Firstly, the squares on the sides of the right triangle are substituted by other geometrically similar planar figures (Euclid's Elements Book VI, Proposition 31 [1]). Secondly, the assumption of the right angle is omitted (the law of cosines), or both of these generalizations occur simultaneously (Pappus’ area theorem [2], see also H. W. Eves [3]). Thirdly, mathematical spaces other than the plane are considered (for example, de Gua-Faulhaber theorem about trirectangular tetrahedra [3], further generalised by Tinseau [4], Euclideann-spaces, Banach spaces [5], see also [6]).

Effect of Heat Treatment Parameters on the Hardness of Soil Working Parts

The experiment of the hardness property for 65Mn spring steel under different heat treatments is conducted. The results are discussed based on the regression orthogonal design. The hardness property of 65Mn steel has been discussed by applying diverse heat treatment technology and the optimum parameters of heat treatment for the best hardness value are obtained through experiments. The influence of the parameters on hardness property is studied by applying the regression orthogonal design. The relation between the hardness and diverse heat treatment parameters has been given by using planar figure. The optimum heat treatment parameter for maximum hardness ability is obtained as following: 851.4°C for quenching temperature, 18 min for quenching time, and 146.4°C for tempering temperature, respectively. The result showed that the selection of material heat treatment process parameters has a great influence on the hardness of the material, which will provide a reliable basis to further study the wear resistance of material.

Elementary and Middle School Children's Comprehension of Euclidean Transformations

A recurring question of interest to curriculum writers and mathematics educators is the following: “What geometry should be taught in the elementary and middle schools, at what age, and in what context?” Substantive recommendations for the inclusion of transformational geometry in the elementary and middle school curriculum have been made and are being implemented. However, there is a scarcity of research data on which to base these innovations. More specifically, little empirical evidence exists concerning the spatial capability of children with respect to Euclidean transformations. Hence, the present study was devised to investigate 9, 11, and 13 year-old children's comprehension of Euclidean transformations; that is, to investigate their ability to form a mental image of a planar figure, to perform a mental operation (a Euclidean transformation) on this representation, and then to construct the resultant in correct position.