Support vector regression for warranty claim forecasting

Forecasting the number of warranty claims is vitally important for manufacturers/warranty providers in preparing fiscal plans. In existing literature, a number of techniques such as log-linear Poisson models, Kalman filter, time series models, and artificial neural network models have been developed. Nevertheless, one might find two weaknesses existing in these approaches: (1) they do not consider the fact that warranty claims reported in the recent months might be more important in forecasting future warranty claims than those reported in the earlier months, and (2) they are developed based on repair rates (i.e., the total number of claims divided by the total number of products in service), which can cause information loss through such an arithmetic-mean operation.To overcome the above two weaknesses, this paper introduces two different approaches to forecasting warranty claims: the first is a weighted support vector regression (SVR) model and the second is a weighted SVR-based time series model. These two approaches can be applied to two scenarios: when only claim rate data are available and when original claim data are available. Two case studies are conducted to validate the two modelling approaches. On the basis of model evaluation over six months ahead forecasting, the results show that the proposed models exhibit superior performance compared to that of multilayer perceptrons, radial basis function networks and ordinary support vector regression models.     

Symmetry and Uniqueness of Solutions of an Integral System

In this paper, we study the positive solutions for a class of integral systems and prove that all the solutions are radially symmetric and monotonically decreasing about some point. Moreover, we also obtain the uniqueness result for a special case. We use a new type of moving plane method introduced by Chen-Li-Ou [1]. Our new ingredient is the use of Hardy-Littlewood-Sobolev inequality instead of Maximum Principle.     

An instrumentation system to measure the loads acting on the tractor PTO bearing during rotary tillage

Application of rotary tillage has been increased due to less tillage passes required, reduced draft, and greater efficiency through reduction in wheel slippage. Early failure of the bearing of tractor power take-off (PTO) shaft was observed in tractors of power range 30–35 horsepower during rotary tillage. An instrumentation setup involving an extended octagonal ring transducer (EORT) was developed and installed at the bottom of the bearing to measure the axial load and the vertical component of the radial load. The horizontal component of radial load was measured by strain gauges. Based on measured loads, the bearing life was assessed. Independent variables were: operating depth, number of blades, gear setting, engine speed, and tyre size. The average axial and radial loads varied from 786–3869 N, and 134–430 N, respectively. However, bearing experienced very high peak loads during each trial. The peak axial and radial loads was recorded between 1081–7534 N and 566–1794 N, respectively. The estimated bearing life based on peak loads was 171.98–28341.39 h. Based on the findings, it may be concluded that the average loads were not sufficient to cause quick failure of PTO bearing, rather sudden peak loads might be the root cause of early failure.     

Radial stereo imaging system for three-dimensional reconstruction

In this paper, we propose a radial stereo imaging system for three-dimensional reconstruction of an object. This system uses a novel optical device which consists of a camera and two reflected mirrors. It can reconstruct three-dimensional model of an object by capturing one image. Depending on the reflection of the mirrors, each world point in the scene has a pair of points which sit in the inner and outer of the captured image, respectively. We firstly analyze the imaging constraint of the proposed system, and then derive the geometrical relationship between world point and image point pair to calculate the three-dimensional coordinate values of an arbitrary point on the object, which means that the three-dimensional model of the object can be recovered. Experiments are carried out to prove our design, and the results show that our radial stereo imaging system is convenient and effective for the three-dimensional reconstruction of an object. This system can be used in variety of applications, such as virtual reality and commodity show.     

HL－1M低混杂波电流驱动中的径向扩散效应

本文利用低混杂波电流驱动的准线性理论模型，研究了由于磁场的随机涨落而引起的快电子的反常输运对驱动电流分布和驱动效率的影响。结果表明，高能电子径向扩散将使驱动电流分布变平和展宽，同时驱动电流减小。     

Calibrating camera radial distortion with cross-ratio invariability

The calibration of camera distortion plays an important role in the field of industrial machine vision application. In this paper, a novel approach for calibrating camera radial distortion is presented based on cross-ratio invariability for perspective projection. Assumed to be with one-order radial distortion, the image coordinates and the cross-ratio of only four collinear points in space are needed in this approach. The cross-ratio, easily known from a calibration target, is identical with that of the four corresponding image points. This is called the cross-ratio invariability for perspective projection. A monadic two-order equation is built based on the cross-ratio invariability, which gives an accurate solution to radial distortion coefficients. A digital simulation and a practical image correction prove this approach to be simple, accurate, efficient and time saving.     

Approximation in rough native spaces by shifts of smooth kernels on spheres

Within the conventional framework of a native space structure, a smooth kernel generates a small native space, and “radial basis functions” stemming from the smooth kernel are intended to approximate only functions from this small native space. Therefore their approximation power is quite limited. Recently, Narcowich et al. (J. Approx. Theory 114 (2002) 70), and Narcowich and Ward (SIAM J. Math. Anal., to appear), respectively, have studied two approaches that have led to the empowerment of smooth radial basis functions in a larger native space. In the approach of [NW], the radial basis function interpolates the target function at some scattered (prescribed) points. In both approaches, approximation power of the smooth radial basis functions is achieved by utilizing spherical polynomials of a (possibly) large degree to form an intermediate approximation between the radial basis approximation and the target function. In this paper, we take a new approach. We embed the smooth radial basis functions in a larger native space generated by a less smooth kernel, and use them to approximate functions from the larger native space. Among other results, we characterize the best approximant with respect to the metric of the larger native space to be the radial basis function that interpolates the target function on a set of finite scattered points after the action of a certain multiplier operator. We also establish the error bounds between the best approximant and the target function.     

Power scaling of diffusion-cooled lasers

An excitation and optical extraction geometry suitable for compact high power gas lasers is described. Multiple slab discharges are established in a diffusion-cooled radial electrode array. Each gain channel is independently driven from a common RF source via a resonant-cavity power distribution system. Radial excitation augmented with multi-channel self-injection phase locking provides stable optical power extraction at good efficiency. The concept is easily scalable to very high powers while dramatically reducing unit size and cost.     

Existence of radial solutions for an asymptotically linear p-Laplacian problem

We prove that an asymptotically linear Dirichlet problem which involves the p-Laplacian operator has multiple radial solutions when the nonlinearity has a positive zero and the range of the ‘p-derivative’ of the nonlinearity includes at least the first j radial eigenvalues of the p-Laplacian operator. The main tools that we use are a uniqueness result for the p-Laplacian operator and bifurcation theory.     

Global existence of solutions for semilinear damped wave equation in 2-D exterior domain

We consider a mixed problem of a damped wave equation u_tt−Δu+u_t=|u|^p in the two dimensional exterior domain case. Small global in time solutions can be constructed in the case when the power p on the nonlinear term |u|^p satisfies p∗=2<p<+∞. For this purpose we shall deal with a radially symmetric solution in the exterior domain. A new device developed in Ikehata-Matsuyama (Sci. Math. Japon. 55 (2002) 33) plays an effective role.