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The ability to forecast a trend is very important in energy consumption prediction and energy production planning. The principle, under which the grey systems theory is applied in our energy consumption prediction, is that the forecasting system can be considered as a grey system. In such a system, unknown system's information can be determined by using known information. Here, the known information consists of energy consumption data, development trend in the consumption system. Based on our study, we eventually make forecast and decisions regarding possible future development. Our method is a whitenization process of a grey course. The model developed is based on the division method established for general data modelling and estimation of parameters of GM(1,1) its standard error coefficient that was applied to judge the accuracy height of the model was put forward; further, the function transform to forecast energy consuming trend and assess GM(1, 1) parameter was established. These two models need not pre‐process the primitive data. It was not only suited for equal interval data modeling, but also for non‐equal interval data modeling. Its calculation was simple and used conveniently, and the oil consumption per unit output analysis was taken as an example. The example showed that the two models were simple and practical, it was worth expanding and applying in the energy consuming prediction and energy programming.

In part I uses an iterative point successive over‐relaxation (PSOR) finite difference scheme to solve the coupled unsteady Navier‐Stokes and energy equations for incompressible, viscous and laminar flows in their primitive variable form. Presents the details concerning the derivation of the solution scheme, as well as details on its computer implementation. For validation purposes, includes the results of the two‐dimensional and three‐dimensional benchmark problem of natural convection in a cavity with differentially heated vertical walls. Benchmark computations have been performed for a Prandtl number of 0.71, and different values of the Rayleigh number ranging between 10³ and 10⁶ depending on the problem. By comparison with other approaches in the literature, the scheme has been found to be accurate even for large Rayleigh numbers.

The purpose of this paper is to describe and analyse a class of finite element fractional step methods for solving the incompressible Navier-Stokes equations. The objective is not to reproduce the extensive contributions on the subject, but to report on long-term experience with and provide a unified overview of a particular approach: the characteristic-based split method. Three procedures, the semi-implicit, quasi-implicit and fully explicit, are studied and compared.

This work provides a thorough assessment of the accuracy and efficiency of these schemes, both for a first and second order pressure split.

In transient problems, the quasi-implicit form significantly outperforms the fully explicit approach. The second order (pressure) fractional step method displays significant convergence and accuracy benefits when the quasi-implicit projection method is employed. The fully explicit method, utilising artificial compressibility and a pseudo time stepping procedure, requires no second order fractional split to achieve second order or higher accuracy. While the fully explicit form is efficient for steady state problems, due to its ability to handle local time stepping, the quasi-implicit is the best choice for transient flow calculations with time independent boundary conditions. The semi-implicit form, with its stability restrictions, is the least favoured of all the three forms for incompressible flow calculations.

A comprehensive comparison between three versions of the CBS method is provided for the first time.

New contact boundary modelling is achieved with a basic set of 2 and 3 dimension contact primitives. Contact constraints are originally introduced in the variational equations and associated Newton—Raphson scheme via an external penalty formulation using primitive equations. Consequently, penalty part of external load vector and tangent stiffness matrices are developed for all contact primitives. In this way, contact prescribed boundary displacements are also taken into account. Contact treatment is then completed with Newton—Raphson elements for elastic and plastic regularized friction constitutive models. In this paper, the process is extended to elastoplastic models. Finally, we propose a self acting procedure with contact algorithms (interiority, sliding and contact loss) and related subroutines for implementation in finite element framework. We illustrate these developments by means of two‐dimensional open die forging and three‐dimensional plate coining typical benchmarks with reference to bulk elastoplastic and viscoplastic constitutive models.

We describe a novel mathematical approach to deriving and solving covolume models of the incompressible 2‐D Navier‐Stokes flow equations. The approach integrates three technical components into a single modelling algorithm: 1. Automatic Grid Generation. An algorithm is described and used to automatically discretize the flow domain into a Delaunay triangulation and a dual Voronoi polygonal tessellation. 2. Covolume Finite Difference Equation Generation. Three covolume discretizations of the Navier‐Stokes equations are presented. The first scheme conserves mass over triangular control volumes, the second scheme over polygonal control volumes and the third scheme conserves mass over both. Simple consistent finite difference equations are derived in terms of the primitive variables of velocity and pressure. 3. Dual Variable Reduction. A network theoretic technique is used to transform each of the finite difference systems into equivalent systems which are considerably smaller than the original primitive finite difference system.

The primitive equations of a barotropic atmosphere in isobaric co‐ordinates are reformulated, in order to express the geopotential gradient as a function of the pressure at the Earth’s surface. Furthermore, the free surface equation is written in conservative form. A finite difference, semi‐implicit, semi‐Lagrangian scheme in isobaric co‐ordinates is developed. The numerical scheme is mass conservative, is proven to be stable and requires the solution of a single five‐diagonal system. Numerical simulations show that the model captures the main dynamical features of large scale atmospheric motion.

It is known that a mathematical ecological model and, in general, a particular methodology of modelling, can be considered a literary text written in a formal mathematical language. In this context, stylometric mathematical laws such as Zipf’s (range‐frequency and number‐frequency) can be applied to obtain information parameters in different semantic levels within the same model. Adapts several of these laws and introduces new elements, lexic units, operating and separating units, to carry out several statistical analyses upon two models or texts. The estimated slopes in the regression equations obtained in the present work are compared with the results of previous papers where Mandelbrot’s law was applied and comparisons between them are shown.

The purpose of this paper is to present a further extension of the regular grammars of the language L(M_T).

This language may represent an ecological model, written in a formal mathematical structure.

The paper presents and develops recognoscitive and generative grammars of sentences (flow equations) together with a synonymy relationship, which characterize the L(M_T) language.

Provides a discussion of modelling of language.

Dynamic movement primitives (DMPs) is a general robotic skill learning from demonstration method, but it is usually used for single robotic manipulation. For cloud-based robotic skill learning, the authors consider trajectories/skills changed by the environment, rebuild the DMPs model and propose a new DMPs-based skill learning framework removing the influence of the changing environment.

The authors proposed methods for two obstacle avoidance scenes: point obstacle and non-point obstacle. For the case with point obstacles, an accelerating term is added to the original DMPs function. The unknown parameters in this term are estimated by interactive identification and fitting step of the forcing function. Then a pure skill despising the influence of obstacles is achieved. Using identified parameters, the skill can be applied to new tasks with obstacles. For the non-point obstacle case, a space matching method is proposed by building a matching function from the universal space without obstacle to the space condensed by obstacles. Then the original trajectory will change along with transformation of the space to get a general trajectory for the new environment.

The proposed two methods are certified by two experiments, one of which is taken based on Omni joystick to record operator’s manipulation motions. Results show that the learned skills allow robots to execute tasks such as autonomous assembling in a new environment.

This is a new innovation for DMPs-based cloud robotic skill learning from multi-scene tasks and generalizing new skills following the changes of the environment.

We describe a new mathematical approach for deriving and solving covolume models of the three‐dimensional, incompressible Navier—Stokes flow equations. The approach integrates three technical components into a single modelling algorothm: automatic grid generation; covolume equation generation; dual variable reduction.