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The purpose of this paper is to discuss a data interpolation method of curved surfaces from the point of dimension reduction and manifold learning.

Instead of transmitting data of curved surfaces in 3D space directly, the method transmits data by unfolding 3D curved surfaces into 2D planes by manifold learning algorithms. The similarity between surface unfolding and manifold learning is discussed. Projection ability of several manifold learning algorithms is investigated to unfold curved surface. The algorithms’ efficiency and their influences on the accuracy of data transmission are investigated by three examples.

It is found that the data interpolations using manifold learning algorithms LLE, HLLE and LTSA are efficient and accurate.

The method can improve the accuracies of coupling data interpolation and fluid-structure interaction simulation involving curved surfaces.

The purpose of this paper is to propose a new temporal disaggregation method for time series based on the accumulated and inverse accumulated generating operations in grey modeling and the interpolation method.

This disaggregation method includes three main steps, including accumulation, interpolation, and differentiation (AID). First, a low frequency flow series is transformed to the corresponding stock series through accumulated generating operation. Then, values of the stock series at unobserved time is estimated through appropriate interpolation method. And finally, the disaggregated stock series is transformed back to high frequency flow series through inverse accumulated generating operation.

The AID method is tested with a sales series. Results shows that the disaggregated sales data are satisfactory and reliable compared with the original data and disaggregated data using a time series model. The AID method is applicable to both long time series and grey series with insufficient information.

The AID method can be easily used to disaggregate low frequency flow series.

The AID method is a combination of grey modeling technique and interpolation method. Compared with other disaggregation methods, the AID method is simple, and does not require auxiliary information or plausible minimizing criterion required by other disaggregation methods.

The purpose of this paper is to examine the effects of user-defined parameters settings (e.g. interpolation method, grid cell size, and bandwidth) on the predictive accuracy of crime hotspot maps produced from kernel density estimation (KDE).

The influence of variations in parameter settings on prospective KDE maps is examined across two types of interpersonal violence (e.g. aggravated assault and robbery) and two types of property crime (e.g. commercial burglary and motor vehicle theft).

Results show that interpolation method has a considerable effect on predictive accuracy, grid cell size has little to no effect, and bandwidth as some effect.

The current study advances the knowledge and understanding of prospective hotspot crime mapping as it answers the calls by Chainey et al. (2008) and others to further investigate the methods used to predict crime.

A magnetization table describing the magnetic properties of the material of interest is the primary input for any computer program expected to calculate magnetic fields or other magnetic parameters in a nonlinear case. Magnetization tables, however, consist of discrete points, and the program assumes some interpolation rule to calculate values between them. There exists a variety of interpolation schemes, and some of them can produce very large errors and even unphysical results when the intervals are not narrow enough. Unfortunately, it was found that intervals used in practice are seldom narrow enough. The accurate interpolation of magnetization tables thus becomes a central issue in the numerical solution of nonlinear magnetic problems. We discuss several interpolation schemes used in practice. We propose a new one that is guaranteed to give physical results, and we address the question as to how wide the table invervals can be if a desired accuracy is specified. The discussion is illustrated with many examples.

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 an automatic interpolation method for binarized confocal laser scanning microscopy (CLSM) images of a premotor neuron in the silkworm moth.

Partial deficiencies occur in binary images through the form extraction process because of noises in a CLSM image series. The proposed method selects several points from a binarized image series and connects these points with a Bezier curve based on premotor neuron characteristics in order to interpolate partial deficiencies.

To verify the availability of the proposed method, a three‐dimensional form of a premotor neuron of a silkworm moth was extracted. The results of each branch's relation of connection and of the interpolated neuron thickness show that the proposed method realizes to interpolate partial deficiencies and to extract three‐dimensional form of the premotor neuron.

The proposed method contributes to realize efficient premotor extraction process using image‐processing techniques. The extracted result by proposed method can be utilized for the form comparison among many data of the premotor neurons quickly. Moreover, it also contributes to provide the parameters of an accurate neuron model for realizing computer simulation of electrical of the neurons.

The proposed method extracts not only a topological form but also a premotor neuron's thickness by interpolating partial deficiencies based on specific characteristics of the neuron. Thickness values of the neuron are an important factor for a simulating accurate electrical response of the neuronal circuit.

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.

The purpose of this paper is to extend the natural neighbour radial point interpolation method (NNRPIM) to the dynamic analysis (free vibrations and forced vibrations) of two‐dimensional, three‐dimensional and bending plate problems.

The NNRPIM shape‐function construction is briefly presented, as are the dynamic equations and the mode superposition method is used in the forced vibration analysis. Several benchmark examples of two‐dimensional and plate bending problems are solved and compared with the three‐dimensional NNRPIM formulation. The obtained results are compared with the available exact solutions and the finite element method (FEM) solutions.

The developed NNRPIM approach is a good alternative to the FEM for the solution of dynamic problems, once the obtained results with the EFGM shows a high similarity with the obtained FEM results and for the majority of the studied examples the NNRPIM results are more close to the exact solution results.

Comparing the FEM and the NNRPIM, the computational cost of the NNRPIM is higher.

The paper demonstrates extension of the NNRPIM to the dynamic analysis of two‐dimensional, three‐dimensional and bending plate problems. The elimination of the shear‐locking phenomenon in the NNRPIM plate bending formulation. The various solved examples prove a high convergence rate and accuracy of the NNRPIM.

Develop a local radial point interpolation method (LRPIM) to analyze the dissipation process of excess pore water pressure in porous media and verify its numerical capability.

Terzaghi's consolidation theory is used to describe the dissipation process. A local residual form is formulated over only a sub‐domain. This form is spatially discretized by radial point interpolation method (RPIM) with basis of multiquadrics (MQ) and thin‐plate spline (TPS), and temporally discretized by finite difference method. One‐dimensional (1D) and two‐dimensional consolidation problems are numerically analyzed.

The LRPIM is suitable, efficient and accurate to simulate this dissipation process. The shape parameters, q=1.03, R=0.1 for MQ and η=4.001 for TPS, are still valid.

The asymmetric system matrix in LRPIM spends more resources in storage and CPU time.

Local residual form requires no background mesh, thus being a truly meshless method. This provides a fast and practical algorithm for engineering computation.

This paper provides a simple, accurate and fast numerical algorithm for the dissipation process of excess pore water pressure, largely simplifies data preparation, shows that the shape parameters from solid mechanics are also suitable for the dissipation process.

To compare slip surface and moving band techniques for modelling movement in 3D with FEM.

The slip surface and moving band techniques are used to model the rotation of electrical machines in 3D with FEM. The proposed techniques are applied to a permanent magnet synchronous machine. The comparison is carried out at no‐load for the electromotive force (EMF) and the cogging torque. The torque is also compared for the short circuit case.

For both the locked‐step and moving band approaches there is no difficulty in establishing the scalar potential and potential vector formulations. However, if step displacement is not equal to the mesh step, the results can show numerical irregularities. Some improvements have been proposed in order to limit this problem.

The results of the EMF and the cogging torque are improved.