Bootstrapping the Local Periodogram of Locally Stationary Processes

Abstract. Locally stationary processes are non‐stationary stochastic processes the second‐order structure of which varies smoothly over time. In this paper, we develop a method to bootstrap the local periodogram of a locally stationary process. Our method generates pseudo local periodogram ordinates by combining a parametric time and non‐parametric frequency domain bootstrap approach. We first fit locally a time varying autoregressive model so as to capture the essential characteristics of the underlying process. A locally calculated non‐parametric correction in the frequency domain is then used so as to improve upon the locally parametric autoregressive fit. As an application, we investigate theoretically the asymptotic properties of the bootstrap method proposed applied to the class of local spectral means, local ratio statistics and local spectral density estimators. Some simulations demonstrate the ability of our method to give accurate estimates of the quantities of interest in finite sample situations and an application to a real‐life data‐set is presented.     

Investigation of Centreline Segregation and Centreline Porosity in CC ‐ Slabs

Improvements of solidification processing in conventional or near net shape casting depend on sophisticated methods of macroscopic examination of central unsoundness and inhomogeneity of the cast material. As long as remarkable deviations referring to the quality features exist between the slab centre and the bulk material such methods should be looked after. Two semi‐macroscopic methods of segregation analysis are discussed in this paper: firstly, the potential of the emission spectral analysis combined with sectioning of a sample and secondly, the computer aided micro‐probe analysis. Both methods are restricted to small local areas. The proneness of elements and steel grades with respect to micro‐ and macrosegregation as well as distribution‐ and segregation coefficients are determined. The effect of a diffusion anneal on homogenisation of segregation is studied. Last not least the precipitation of sulphides, phosphides or carbonitrides is estimated. Ultrasonic detection of the central unsoundness of conventional slabs or thin slabs is a new approach towards a quantitative macroscopic examination. The sample size is 400 mm x 300 mm x 30 mm. To achieve a low ultrasonic noise using a 5 MHz‐transducer the samples are heat treated for grain refinement. “Dog bone porosity”, macroscopic topographical misfit between the upper and lower solidifying shells, periodical corner cracks or systematic transverse centre cracks are detected. Obviously, segregations do not reflect the ultrasonic beam. However, it can be presumed that an interrelation exists between porosity and segregation, although these might be locally apart from each other. This new ultrasonic test of the central unsoundness of continuous cast (c.c.) slabs gives valuable arguments to machine builders and maintenance people to decide on the right concepts for strand guidance, support rollers and secondary cooling. Soft reduction can be optimized and variations in casting speed counteracted by dynamic means. R&D service of this kind can help steelmakers when decisions are impending to build new casting machines or revamp old ones.     

关于彩色火焰蜡烛的研制

本文阐述了利用焰色反应的原理研制彩色火焰蜡烛，着重分析并解决了在研制工作中出现的几个技术关键，如主燃剂的选取、蜡烛成型和强度、发色剂的选择与用量等．     

A NEW ALGORITHM FOR ADAPTIVE LATTICE FILTERAND ITS APPLICATION IN THE SPEECH LINEARPREDICTIVE SYNTHESIS

In this paper, an adaptive line spectral pair filter is derived from an adaptive lattice filter. A least-mean-square(LMS) type adaptive algorithm used to calculate directly the line spectral pair(LSP) coefficients on a stage-by-stage basis is presented. Experimental results show that the algorithm has higher convergence rate and lower misadjustment as compared with the other algorithms. The LSP coefficients calculated by the algorithm have been used to carry out speech linear predictive synthesis, resulting in better results than PARCOR coefficients.     

Comments on the shortcomings of predicting the precision of Cavalieri volume estimates based upon assumed measurement functions

It is well known that the estimation of an object's volume by means of serial cross-sections, the so-called Cavalieri method, yields an unbiased estimate. But by itself it provides no means by which to estimate how precise this estimate is unless the shape of the volume is fully known beforehand. This knowledge can only be partially determined from the serial section information that is collected. Methods have been developed that claim to surmount this difficulty by using the serial section data to create a mathematical model of the volume's shape properties. The model then is used to estimate (predict) the precision of the volume estimate (its CE) from the single set of data available. Unfortunately, the theory underlying the model is flawed and so the model itself amounts to no more than an unsubstantiated guess about the shape of the volume. Therefore, the precision of the volume estimates that one obtains from the method is only as good as the model and this cannot be ascertained from the single set of acquired data. In this letter I explain the inadequacies of the modelling method. I suggest that it be used only with caution, if at all. Instead I suggest two alternative ways to predict the CE, one that is based upon a rule-of-thumb approach to the object's shape, and another that is based upon spectral analysis of the measurement function and that is easy to implement with available computer software.     

Variations in Spectral Slope in Lake Taihu,a Large Subtropical Shallow Lake in China

Spectral slope (S), describing the exponential decrease of the absorption spectrum over a given wavelength range, is an important parameter in the study of of chromophoric dissolved organic matter (CDOM) dynamics, and also an essential input parameter in remote sensing models. Furthermore, S is often used as a proxy for CDOM composition, including the ratio of fulvic to humic acids and molecular weight. The relative broad range in S values reported in the literature can be explained by the different spectral ranges and fitting methods used. A single exponential model is used to fit the S values for 17 investigations involving 458 samples in Lake Taihu from January to October in 2004. The average S value was 15.18 ± 1.39 μm⁻¹ for the range of 280–500 nm, which fell within the range reported in the literature. The frequency distribution of S value basically obeyed a normal distribution. Significant differences in S values between summer and other seasons showed that phytoplankton degradation was one of the important sources of CDOM in summer, whereas CDOM mainly came from the river input in other seasons. Furthermore, the estimated S value decreased with increasing wavelength range used in regression. The maximum and minimum values derived from the regression were 17.89 ± 1.25 μm⁻¹ and 13.62 ± 2.11 μm⁻¹ for the wavelength ranges of 280–380 nm and 400–500 nm, respectively, a decrease of 23.9%. S values significantly decreased with the increase of CDOM absorption coefficients. CDOM absorption coefficients could be more appropriately estimated from exponential model introducing the variation of S with absorption coefficients, making them useful for a remote sensing bio-optical model of Lake Taihu. DOC-specific absorption coefficient a*(λ) and the parameter M describing molecular size of the humic molecules could also be used as a proxy for the sources and types of CDOM. A general relationship was found between S and a*(λ), and M values. S increased with the decrease of DOC-specific absorption coefficient and the increase of M corresponding to the decrease of molecular weight.     

Reconstruction of a discontinuous function from a few fourier coefficients using bayesian estimation

The goal of this paper is the application of spectral methods to the numerical solution of conservation law equations. Spectral methods furnish estimates of the firstn Fourier coefficients of the solution. But since the solutions of conservation law equations can have discontinuities, the estimate of the solution by summing the firstn terms of the Fourier series will haveO(1/n) error, even if the Fourier coefficients are known to high accuracy. But if the solution could be accurately reconstructed from its Fourier coefficients, spectral methods could be used effectively in these problems. A method for doing this is to assume a probability distribution for functions. Functions which are smooth away from the discontinuity are assumed to be likely, and those which are not smooth away from the discontinuity are assumed to be unlikely. Then a reconstruction algorithm is chosen by minimizing the expected error over all algorithms. It is possible to put the smoothness assumptions mentioned earlier into an infinite-dimensional Gaussian probability distribution, and then the minimum-error algorithm is well-known and fairly simple to construct and apply. If the Fourier coefficients of the reconstructed function are known exactly, then this approach gives very good results. But when used with Fourier coefficients obtained from a spectral approximation to Burgers' equation, the results were much less impressive, probably because the coefficients were not known very accurately. It is possible to construct filters that reconstruct a function using Legendre or Chebyshev coefficients for information instead Fourier coefficients. It is found that the performance of these filters is similar to the Fourier case.     

岩石声学参数测量分析系统

刘祝萍等．岩石声学参数测量分析系统．测井技术，１９９４，１８（４）：２８８～２９８岩石声学参数测量是声波测井资料解释的基础性工作。本文介绍一种岩样声学参数测量分析系统，该系统能对岩样的纵（Ｐ）、横（Ｓ）波速度进行测量记录，并可将实测波形进入计算机，对所记录的波形进行频谱分析后，通过与标准试件的比较，可估算岩样的声衰减。     

Spectral projective newton-methods for quasilinear elliptic boundary value problems

We consider Newton-like methods for the solution of quasilinear elliptic boundary value problems. The quasilinear problems are linearized by a Newton-method and the linear problems are approximately solved by a spectral projection method (e.g., the Ritz-Galerkin or the collocation method). convergence results are derived that show the spectral accuracy of this method. The results are of a local type which means that we assume the starting approximation to be sufficiently near to the exact solution.     

计及PMU的混合非线性状态估计新方法

提出一种将同步相量测量单元（PMU）的直接电压相量量测变换为间接支路电流量测，并与监控与数据采集（SCADA）量测量一起进行混合迭代的非线性状态估计方法。对构造等效电流修正量而带来的间接量测误差进行了详细和定量的分析，并对该混合估计算法的精度进行了定性分析和定量计算。理论分析和算例表明，该方法可以获得较高的估计精度，在收敛次数和滤波效果上也有所改进。