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To propose trigonometric interpolation in combination with both sliding‐surface and moving‐band techniques for modelling rotation in finite‐element electrical machine models. To show that trigonometric interpolation is at least as accurate and efficient as standard stator‐rotor coupling schemes.

Trigonometric interpolation is explained concisely and put in a historical perspective. Characteristic drawbacks of trigonometric interpolation are alleviated one by one. A comparison with the more common locked‐step linear‐interpolation and mortar‐element approaches is carried out.

Trigonometric interpolation offers a higher accuracy and therefore can outperform standard stator‐rotor coupling techniques when equipped with an appropriate iterative solver incorporating Fast Fourier Transforms to reduce the higher computational cost.

The synthetic interpretation of trigonometric interpolation as a spectral‐element approach in the machine's air gap, the efficient iterative solver combining conjugate gradients with Fast Fourier Transforms. The unified application to both sliding‐surface and moving‐band techniques.

The purpose of this paper is to solve the trajectory planning problem of industrial robots in a complex environment.

A simultaneous algorithm was presented in which the trajectory was generated gradually as the robot moves. It takes into account the presence of obstacles (to avoid collisions) and differential constraints related to the dynamics of the robotic system. The method poses an optimization problem that aims at minimizing the time to perform the trajectory when several interpolation functions are used.

A new approach to solving the trajectory planning problem in which the behaviour of four operational parameters (execution time, computational time, distance travelled and number of configurations) have been analyzed when changing the interpolation functions, therefore enabling the user to choose the most efficient algorithm depending on which parameter the user is most interested in. From the examples solved the interpolation function that yields the best results has been found.

This new technique is very time consuming due to the great number of mathematical calculations that have to be made. However, it yields a solution.

The algorithm is able to obtain the solution to the trajectory planning problem for any industrial robot. Also, even mobile obstacles in the workspace could be incorporated at the same time as the robot is moving and creating the path and the time history of motion.

It gives a new tool for solving the trajectory planning problem and describes the best interpolation function.

The purpose of this paper is to develop an application software interpolation system based on Taylor Kriging (TK) metamodeling, and apply the developed software system to addressing some engineering interpolation problems.

TK is a novel Kriging model where Taylor expansion is used to identify the base functions of drift function in Kriging. The paper explains the methodology of TK, illustrates the development of software, and reports the results of two case studies by comparing TK with several regression methods.

TK has the advantage of interpolation accuracy, and the developed Kriging software system is useful and can be conveniently manipulated by users.

The developed software system can benefit practical engineering applications that need accurate interpolations under limited observations.

This paper develops an application software interpolation system based on a novel TK metamodel, and the practical engineering applications show that it can provide accurate interpolations under limited observations.

This paper is concerned with the application of radial basis function networks (RBFNs) as interpolation functions for all boundary values in the boundary element method (BEM) for the numerical solution of heat transfer problems. The quality of the estimate of boundary integrals is greatly affected by the type of functions used to interpolate the temperature, its normal derivative and the geometry along the boundary from the nodal values. In this paper, instead of conventional Lagrange polynomials, interpolation functions representing these variables are based on the “universal approximator” RBFNs, resulting in much better estimates. The proposed method is verified on problems with different variations of temperature on the boundary from linear level to higher orders. Numerical results obtained show that the BEM with indirect RBFN (IRBFN) interpolation performs much better than the one with linear or quadratic elements in terms of accuracy and convergence rate. For example, for the solution of Laplace's equation in 2D, the BEM can achieve the norm of error of the boundary solution of O(10⁻⁵) by using IRBFN interpolation while quadratic BEM can achieve a norm only of O(10⁻²) with the same boundary points employed. The IRBFN‐BEM also appears to have achieved a higher efficiency. Furthermore, the convergence rates are of O(h^1.38) and O(h^4.78) for the quadratic BEM and the IRBFN‐based BEM, respectively, where h is the nodal spacing.

A finite volume scheme for diffusion equations on non-rectangular meshes is proposed in [Deyuan Li, Hongshou Shui, Minjun Tang, J. Numer. Meth. Comput. Appl., 1(4)(1980)217–224 (in Chinese)], which is the so-called nine point scheme on structured quadrilateral meshes. The scheme has both cell-centered unknowns and vertex unknowns which are usually expressed as a linear weighted interpolation of the cell-centered unknowns. The critical factor to obtain the optimal accuracy for the scheme is the reconstruction of vertex unknowns. However, when the mesh deformation is severe or the diffusion tensor is discontinuous, the accuracy of the scheme is not satisfactory, and the author hope to improve this scheme.

The authors propose an explicit weighted vertex interpolation algorithm which allows arbitrary diffusion tensors and does not depend on the location of discontinuity. Both the derivation of the scheme and that of vertex reconstruction algorithm satisfy the linearity preserving criterion which requires that a discretization scheme should be exact on linear solutions. The vertex interpolation algorithm can be easily extended to 3 D case.

Numerical results show that it maintain optimal convergence rates for the solution and flux on 2 D and 3 D meshes in case that the diffusion tensor is taken to be anisotropic, at times heterogeneous, and/or discontinuous.

This paper proposes a linearity preserving and explicit weighted vertex interpolation algorithm for cell-centered finite volume approximations of diffusion equations on general grids. The proposed finite volume scheme with the new interpolation algorithm allows arbitrary continuous or discontinuous diffusion tensors; the final scheme is applicable to arbitrary polygonal grids, which may have concave cells or degenerate ones with hanging nodes. The final scheme has second-order convergence rate for the approximate solution and higher than first-order accuracy for the flux on 2 D and 3 D meshes. The explicit weighted interpolation algorithm is easy to implement in three dimensions in case that the diffusion tensor is continuous or discontinuous.

The purpose of this paper is to propose an interpolation-based projection framework for model reduction of quadratic-bilinear systems. The approach constructs projection matrices from the bilinear part of the original quadratic-bilinear descriptor system and uses these matrices to project the original system.

The projection matrices are constructed by viewing the bilinear system as a linear parametric system, where the input associated with the bilinear part is treated as a parameter. The advantage of this approach is that the projection matrices can be constructed reliably by using an a posteriori error bound for linear parametric systems. The use of the error bound allows us to select a good choice of interpolation points and parameter samples for the construction of the projection matrices by using a greedy-type framework.

The results are compared with the standard quadratic-bilinear projection methods and it is observed that the approximations through the proposed method are comparable to the standard method but at a lower computational cost (offline time).

In addition to the proposed model order reduction framework, the authors extend the one-sided moment matching parametric model order reduction (PMOR) method to a two-sided method that doubles the number of moments matched in the PMOR method.

The purpose of this paper is to simplify the Explicit Nonlinear Model Predictive Controller (ENMPC) by linearizing the trajectory with Quantum-behaved Pigeon-Inspired Optimization (QPIO).

The paper deduces the nonlinear model of the quadrotor and uses the ENMPC to track the trajectory. Since the ENMPC has high demand for the state equation, the trajectory needed to be differentiated many times. When the trajectory is complicate or discontinuous, QPIO is proposed to linearize the trajectory. Then the linearized trajectory will be used in the ENMPC.

Applying the QPIO algorithm allows the unequal distance sample points to be acquired to linearize the trajectory. Comparing with the equidistant linear interpolation, the linear interpolation error will be smaller.

Small-sized quadrotors were adopted in this research to simplify the model. The model is supposed to be accurate and differentiable to meet the requirements of ENMPC.

Traditionally, the quadrotor model was usually linearized in the research. In this paper, the quadrotor model was kept nonlinear and the trajectory will be linearized instead. Unequal distance sample points were utilized to linearize the trajectory. In this way, the authors can get a smaller interpolation error. This method can also be applied to discrete systems to construct the interpolation for trajectory tracking.

The purpose of this paper is to propose a smooth double-spline interpolation method for six-degree-of-freedom rotational robot manipulators, achieving the global C2 continuity of the robot trajectory.

This paper presents a smooth double-spline interpolation method, achieving the global C2 continuity of the robot trajectory. The tool center positions and quaternion orientations are first fitted by a cubic B-spline curve and a quartic-polynomial-based quaternion spline curve, respectively. Then, a parameter synchronization model is proposed to realize the synchronous and smooth movement of the robot along the double spline curves. Finally, an extra u-s function is used to record the relationship between the B-spline parameter and its arc length parameter, which may reduce the feed rate fluctuation in interpolation. The seven segments jerk-limited feed rate profile is used to generate motion commands for algorithm validation.

The simulation and experimental results demonstrate that the proposed method is effective and can generate the global C2-continuity robot trajectory.

The main contributions of this paper are as follows: guarantee the C2 continuity of the position path and quaternion orientation path simultaneously; provide a parameter synchronization model to realize the synchronous and smooth movement of the robot along the double spline curves; and add an extra u-s function to realize arc length parameterization of the B-spline path, which may reduce the feed rate fluctuation in interpolation.

The purpose of the method is to develop a numerical method for the solution of nonlinear partial differential equations.

A new numerical approach based on Barycentric Rational interpolation has been used to solve partial differential equations.

A numerical technique based on barycentric rational interpolation has been developed to investigate numerical simulation of the Burgers’ and Fisher’s equations. Barycentric interpolation is basically a variant of well-known Lagrange polynomial interpolation which is very fast and stable. Using semi-discretization for unknown variable and its derivatives in spatial direction by barycentric rational interpolation, we get a system of ordinary differential equations. This system of ordinary differential equation’s has been solved by applying SSP-RK43 method. To check the efficiency of the method, computed numerical results have been compared with those obtained by existing methods. Barycentric method is able to capture solution behavior at small values of kinematic viscosity for Burgers’ equation.

To the best of the authors’ knowledge, the method is developed for the first time and validity is checked by stability and error analysis.

The purposes of this research are to study the theory and method of multi-attribute index system design and establish a set of systematic, standardized, scientific index systems for the design optimization and inspection process. The research may form the basis for a rational, comprehensive evaluation and provide the most effective way of improving the quality of management decision-making. It is of practical significance to improve the rationality and reliability of the index system and provide standardized, scientific reference standards and theoretical guidance for the design and construction of the index system.

Using modern methods such as complex networks and machine learning, a system for the quality diagnosis of index data and the classification and stratification of index systems is designed. This guarantees the quality of the index data, realizes the scientific classification and stratification of the index system, reduces the subjectivity and randomness of the design of the index system, enhances its objectivity and rationality and lays a solid foundation for the optimal design of the index system.

Based on the ideas of statistics, system theory, machine learning and data mining, the focus in the present research is on “data quality diagnosis” and “index classification and stratification” and clarifying the classification standards and data quality characteristics of index data; a data-quality diagnosis system of “data review – data cleaning – data conversion – data inspection” is established. Using a decision tree, explanatory structural model, cluster analysis, K-means clustering and other methods, classification and hierarchical method system of indicators is designed to reduce the redundancy of indicator data and improve the quality of the data used. Finally, the scientific and standardized classification and hierarchical design of the index system can be realized.

The innovative contributions and research value of the paper are reflected in three aspects. First, a method system for index data quality diagnosis is designed, and multi-source data fusion technology is adopted to ensure the quality of multi-source, heterogeneous and mixed-frequency data of the index system. The second is to design a systematic quality-inspection process for missing data based on the systematic thinking of the whole and the individual. Aiming at the accuracy, reliability, and feasibility of the patched data, a quality-inspection method of patched data based on inversion thought and a unified representation method of data fusion based on a tensor model are proposed. The third is to use the modern method of unsupervised learning to classify and stratify the index system, which reduces the subjectivity and randomness of the design of the index system and enhances its objectivity and rationality.