Formal method for planning the machining of ship machine parts

При разработке технологии изготовления судовых машин, узлов и деталей используются типовые процессы-аналоги, либо описание опыта исполнителей. Известные зарубежные подходы также используют вариативный подход, основанный на типовых решениях, либо генеративный, который предусматривает как формализацию процесса проектирования, так и использование искусственного интеллекта. Как показано в статье одной из основных проблем формализации проектирования технологических процессов является невозможность однозначного представления геометрической конфигурации реальных деталей средствами современной классической геометрии. Для решения этой проблемы предлагается использовать геометрию неидеальных объектов, базисом которой является шестимерное пространство, объединяющее три линейных и три угловых измерения. Использование указанной геометрии позволило определить формальные связи между конструкцией детали и технологическим процессом её изготовления. В статье излагается разработанный авторами метод формального проектирования процессов обработки деталей на станках. Выявленные закономерности порождения геометрических конфигураций позволили разработать алгоритмы генерирования множества методов формообразования элементарных поверхностей. Также определены условия обеспечения сходимости алгоритма формирования комплектов технологических баз и последовательности их выполнения. Изложение материалов подтверждено рассмотрением процесса проектирования технологии обработки на примере реальной детали. When developing a technology for the manufacture of ship machines, units and parts, group processes are used, or a description of the experience of the performers. Well-known foreign approaches also use a variable approach based on standard solutions, or a generative one, which provides for both the formalization of the design process and the use of artificial intelligence. Main problem of formalizing the design of technological processes is the impossibility of an unambiguous representation of the geometric configuration of real parts by means of modern classical geometry. As a solution to this problem, it is proposed to use the geometry of non-ideal objects, the basis of which is a six-dimensional space that combines three linear and three angular dimensions. This geometry made it possible to determine the formal relationships between the design of the part and the technological process of its manufacture. Article describes the method developed by the authors for the formal design of the processing of parts on machine tools. Revealed patterns generation configurations of geometric made it possible to develop algorithms for formation a variety of methods for shaping elementary surfaces. Conditions for ensuring the convergence of algorithm for formation of sets of technological bases and the sequence of their implementation are determined. Presentation materials is confirmed by considering generating of technology using the example of a real part.

Convergence results for fixed point iterative algorithms in metric spaces

In this paper we give some conditions on fn and f which imply the convergence of algorithm (2). In this way we improve some results given in [Rus, I. A., An abstract point of view on iterative approximation of fixed points: impact on the theory of fixed point equations, Fixed Point Theory, 13 (2012), No. 1, 179–192]. In our results, in general we do not suppose that, Ff 6= ∅. Some research directions are formulated.

Neural Gas Clustering Adapted for Given Size of Clusters

Clustering algorithms belong to major topics in big data analysis. Their main goal is to separate an unlabelled dataset into several subsets, with each subset ideally characterized by some unique characteristic of its data structure. Common clustering approaches cannot impose constraints on sizes of clusters. However, in many applications, sizes of clusters are bounded or known in advance. One of the more recent robust clustering algorithms is called neural gas which is popular, for example, for data compression and vector quantization used in speech recognition and signal processing. In this paper, we have introduced an adapted neural gas algorithm able to accommodate requirements for the size of clusters. The convergence of algorithm towards an optimum is tested on simple illustrative examples. The proposed algorithm provides better statistical results than its direct counterpart, balancedk-means algorithm, and, moreover, unlike the balancedk-means, the quality of results of our proposed algorithm can be straightforwardly controlled by user defined parameters.

Wavelet-Based Immune Fuzzy C-Means Algorithm

Fuzzy clustering can express the ambiguity ofsample category, and better reflect the actual needs of datamining. By introducing wavelet transform and artificial immunealgorithm to fuzzy clustering, Wavelet-based Immune Fuzzy C-means Algorithm (WIFCM) is proposed for overcoming theimperfections of fuzzy clustering, such as falling easily into localoptimal solution, slower convergence speed and initialization-dependence of clustering centers. Innovations of WIFCM arethe elite extraction operator and the descent reproductive mode.Using the locality and multi-resolution of wavelet transform, theelite extraction operator explores the distribution and densityinformation of spatial data objects in multi-dimensional spaceto guide the search of cluster centers. Taking advantage ofthe relationship between the relative positions of elite centersand inferior centers, the descent reproductive mode obtains theapproximate fastest descent direction of objective function values,and assures fast convergence of algorithm. Compared to theclassic fuzzy C-means algorithm, experiments on 3 UCI data setsshow that WIFCM has obvious advantages in average numberof iterations and accuracy.

The Convergence Mechanism and Strategies for Non-Elitist Genetic Programming

Genetic programming is an evolutionary algorithm that proposed to solve the automatic computer program design problem by J.R.Koza in the 1990s. It has good universality and intelligence, and has been widely applied in the field of computer engineering. But genetic programming is essentially a stochastic optimization algorithm, lack theoretic basis on the convergence of algorithm, which limit the scope of its application in some extent. The convergence mechanism of non-elitist genetic programming was studied in this paper. A recursive estimation of the probability of population contains satisfactory solution with the evolution algebra was established by the analysis of operators characteristic parameters, then a sufficient condition of population converge in probability was derived from this estimation, and thereby some operational convergence strategies for many common evolution modes were provided.

An Optimised Signal Reconstruction Algorithm for Compressed Sensing

Signal recovery is a key issue in compressed sensing field. A new greedy reconstruction algorithm termed Optimised Stagewise Orthogonal Matching Pursuit (OSOMP) is proposed, which is an improved version for Stagewise Orthogonal Matching Pursuit (StOMP). In preselection step, OSOMP chooses several coordinates with a calculated threshold to accelerate the convergence of algorithm. In following pruning step, a small proportion of selected coordinates are discarded according to the amplitude of estimated signal, thus most false discovered coordinates can be swept away. Experimental results show that in OSOMP, the scale of estimated support can be controlled very well, and the successful recovery rate is also much higher than that in StOMP.

Defaultable Binary Tree Algorithm for Convertible Bond with Finite Maturity

The credit risk is introduced into the pricing model of convertible bond in this paper. The main results of paper have three aspects: (1) By modifying the dynamic motion of stock, a defaultable stock process is obtained in neutral risk measure, then the pricing model of convertible bond with finite maturity and credit is proposed. (2) The defaultable binary tree algorithm is proposed, and the convergence of algorithm is proved.

On the Classification and Existence of Structures in Default Logic1

We investigate possible belief sets of an agent reasoning with default rules. Besides of Reiter’s extensions which are based on a proof-theoretic paradigm (similar to Logic Programming), other structures for default theories, based on weaker or different methods of constructing belief sets are considered, in particular, weak extensions and minimal sets. The first of these concepts is known to be closely connected to autoepistemic expansions of Moore, the other to minimal stable autoepistemic theories containing the initial assumptions. We introduce the concept of stratifed collection of default rules and investigate the properties of the largest stratified subset of the family D, determined by W. We find a necessary and sufficient condition for a weak extension to be an extension in terms of stratification. We prove that for theories (D, W) without extension, the least fixed point of the associated operator (with weak extension or minimal set as a context) is an extension of suitably chosen (D’, W) with D’ ⊆ D. We investigate conditions for existence of extensions and introduce the notion of perfectly-stratified set of default rules and its variant of maximally perfectly-stratified set. Existence of such set of default rules turns out to be equivalent to the existence of extension. Finally, we investigate convergence of algorithm for computing extensions.