The research on drillstring dynamics is necessary for improving drilling efficiency and safety. In this investigation, a multibody dynamical model for 3D full hole drillstring system is presented based on the Absolute Nodal Coordinate Formulation (ANCF). The drillstring is modeled with the ANCF beam element. The absolute nodal coordinate formulation of the beam element as well as the boundary conditions at the top-drive and drill-bit, and the contact/friction model between drillstring and wellbore are also investigated. The dynamic governing equation for full hole drillstring system is given and solved by the backward differentiation formulation (BDF) for differential algebraic equations (DAEs). The developed multibody dynamic solver is capable of analyzing full coupled vibration for the full hole drillstring system. It can play a certain role in drillstring dynamics researches and engineering applications.

Purpose The purpose of this paper is to study distance measuring and sorting method of general grey number. Design/methodology/approach First, the concept of generalised grey number based on grey system theory is given in this paper. Second, from the perspective of kernel and degree of greyness of general grey number, the method of measuring the distance of general grey number and its properties are given. At the same time, the concepts of the kernel expectation and the kernel variance of the general grey number are proposed. Findings Up to now, the method of measuring the distance and sorting of general grey number is established. Thus, the difficult problem for set up sorting of general grey number has been solved to a certain degree. Research limitations/implications The method exposed in this paper can be used to integrate information form a different source. Distance measuring and sorting method of general grey number could be extended to the case of grey algebraic equation, grey differential equation and grey matrix which includes general grey numbers, etc. Originality/value The concepts of the kernel expectation and the kernel variance of the general grey number are proposed for the first time in this paper; the novel sorting rules of general grey numbers were also constructed.

PurposeThe purpose of this paper is to study the grey decision model and distance measuring method of general grey number.Design/methodology/approachFirst, intuitionistic grey number (IGN) set and an IGN are defined by grey number probability function. Second, each interval grey number in general grey number is represented by an IGN and converts the general grey number into an IGN set. Final, the operation of two general grey numbers is defined as the operation between IGN sets, and the distance measure of the general grey number is given.FindingsUp to now, the method of measuring the distance and the grey decision model of general grey number is established. Thus, the difficult problem for set up decision mode of general grey number has been solved to a certain degree.Research limitations/implicationsThe method exposed in this paper can be used to integrate information form a different source. The method that a general grey number converted to a set of IGNs could be extended to the case of grey incidence analysis models, grey prediction models and grey clustering evaluation models, which includes general grey numbers, etc.Originality/valueThe concepts of IGN and IGN set are proposed for the first time in this paper; The operation of two general grey numbers can be defined as the operation between IGN sets. On this basis, the algorithm of IGN, the integration operator of IGN and the distance measure between IGN sets are given.

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