Hidden Frequency Estimation with Data Tapers

The detection and estimation of hidden frequencies has long been recognized as an important problem in time series. In this paper we study the asymptotic theory for two methods of high-precision estimation of hidden frequencies (the secondary analysis method and the maximum periodogram method) using a data taper. In ordinary situations, a data taper may reduce the estimation precision slightly. However, when there are high peaks in the spectral density of the noise or other strong hidden periodicities with frequencies close to the hidden frequency of interest, the procedures for detection of the existence of and estimation of the hidden frequency of interest fail if data are nontapered whereas they may work well if the data are tapered. The theoretical results are verified by some simulated examples.     

基于自动谱聚类与多极端学习机模型的油井油液含水率软测量

油井油液的含水率是石油生产中的一个重要参数,及时、准确的测量对提高采油生产效率具有重要的意义。针对传统人工测量所存在的不足,引入软测量技术,建立基于自动谱聚类与多极端学习机（automatic spectral clustering-multiple extreme learning machines, ASC-MELM）的软测量模型。提出一种自动谱聚类（spectral clustering, SC）算法,由改进的萤火虫算法（firefly algorithm, FA）对聚类数目和尺度参数进行优化选取,所提出的改进萤火虫算法（improved firefly algorithm, IFA）采用以一定概率跳出当前解的机制,避免传统FA过早陷入局部最优解的不足;对聚类后的不同训练子集,分别由极端学习机（extreme learning machine, ELM）建立子模型,由IFA对其中的隐含层输入权值、隐含层神经元的偏置和隐含层节点个数进行优化选取;最后,将多个子模型的结果取加权平均值输出。由国内某油田作业区一口生产井进行实例验证,结果表明所提出方法具有较高的预测精度,对于实现油井油液含水率的软测量是合理有效的。     

Testing the Fit of a Vector Autoregressive Moving Average Model

Abstract. A new procedure for testing the fit of multivariate time series model is proposed. The method evaluates in a certain way the closeness of the sample spectral density matrix of the observed process to the spectral density matrix of the parametric model postulated under the null and uses for this purpose nonparametric estimation techniques. The asymptotic distribution of the test statistic is established and an alternative, bootstrap‐based method is developed in order to estimate more accurately this distribution under the null hypothesis. Goodness‐of‐fit diagnostics useful in understanding the test results and identifying sources of model inadequacy are introduced. The applicability of the testing procedure and its capability to detect lacks of fit is demonstrated by means of some real data examples.     

PEAK-INSENSITIVE NON-PARAMETRIC SPECTRUM ESTIMATION

Abstract. We study the problem of non-parametric spectrum estimation of a stationary time series that might contain periodic components. In this case the periodogram ordinates have a significant amplitude at frequencies near the frequencies of the periodic components. These can be regarded as outliers in an asymptotically exponential sample. We develop a non-parametric estimator for the spectral density that is insensitive to these outliers in the frequency domain. This is done by robustifying the usual kernel estimator (smoothed periodogram) by means of M-estimation in the frequency domain. We propose to use data-tapered periodograms, which yield a drastic improvement of the procedure, typically for the contaminated situation. This is both shown theoretically and supported by means of simulation. We show consistency of the resulting estimator in the general case, and asymptotic normality in the special case of a Gaussian time series, whether contamination is present or not. Finally we illustrate the finite sample performance of the estimating procedure by some simulation results and by application to the Canadian lynx trappings data.     

Composite Quantile Periodogram for Spectral Analysis

We propose a new type of periodogram for identifying hidden frequencies and providing a better understanding of the frequency behaviour. The quantile periodogram by Li ( 2012 ) provides richer information on the frequency of signal than a single estimation of the mean frequency does. However, it is difficult to find a specific quantile that identifies hidden frequencies. In this study, we consider a weighted linear combination of quantile periodograms, termed 'composite quantile periodogram'. It is completely data adaptive and does not require prior knowledge of the signal. Simulation results and real‐data example demonstrate significant improvement in the quality of the periodogram.     

Real-Time Monitoring of Gas–Solid Fluidized-Bed Granulation and Coating Process: Evolution of Particle Size,Fluidization Regime Transitions,and Psychometric Parameters

Moisture content and particle size are critical parameters in fluidized-bed granulation and coating. In this study, microcrystalline cellulose was granulated and coated. The particle size was monitored in real time by a Parsum IPP70 probe. The fluidization regime was assessed by Gaussian spectral analysis. The bed temperature and gas humidity profile were monitored to evaluate the drying efficiency. The defluidization phase was detected in the early stages with frequencies below 6.0 Hz. The Parsum probe showed the growth of the particles due to agglomeration. The psychometric parameters indicated the lower potential energy for drying. Therefore, monitoring in real time is important to detect failures.     

Kinetic study on the first stage during thermal degradation of polystyrene

The kinetic parameters of the first stage of polystyrene degradation have been investigated to elucidate the reaction mechanisms using the flow reactor system. The decrease in molecular weight of polystyrene was recorded at minute intervals over the temperature range 310°–390°C. Generally, the first and second stages were observed by thermogravimetric analysis (t.g.a.), however in the early stage of the degradation volatile yields of at least 5% occurred. Therefore, using t.g.a. analysis it is difficult to detect this earlier stage. It became evident that the first stage in the earlier part of the reaction could be detected by g.p.c. analysis. We have observed the hidden kinetic parameters of the nature of the first stage of the polystyrene degradation. The results indicate that the main chains were degraded randomly with the small quantitative volatile groups in the first stage and the rates of decrease in molecular weight in the first stage against reaction temperatures were evaluated as log k_s = 12.0 ? 41300/RT.     

Generalized Resampling Scheme With Application to Spectral Density Matrix in Almost Periodically Correlated Class of Time Series

The aim of this article is to introduce new resampling scheme for nonstationary time series, called generalized resampling scheme (GRS). The proposed procedure is a generalization of well known in the literature subsampling procedure and is simply related to existing block bootstrap techniques. To document the usefulness of GRS, we consider the example of model with almost periodic phenomena in mean and variance function, where the consistency of the proposed procedure was examined. Finally, we prove the consistency of GRS for the spectral density matrix for nonstationary, multivariate almost periodically correlated time series. We consider both zero mean and non‐zero mean case. The consistency holds under general assumptions concerning moment and α‐mixing conditions for multivariate almost periodically correlated time series. Proving the consistency in this case poses a difficulty since the estimator of the spectral density matrix can be interpreted as a sum of random matrixes whose dependence grow with the sample size.     

DISCRIMINATING BETWEEN TWO SPECTRAL DENSITIES IN CASE OF REPLICATED OBSERVATIONS

Abstract. Coates and Diggle (1986) introduced a test procedure for the comparison of the spectral densities of two stationary processes. We extend this test to a situation in which replicated observations are available for each process.     

LOCALLY ADAPTIVE LAG-WINDOW SPECTRAL ESTIMATION

Abstract. We propose a procedure for the locally optimal window width in nonparametric spectral estimation, minimizing the asymptotic mean square error at a fixed frequency Λ of a lag-window estimator. Our approach is based on an iterative plug-in scheme. Besides the estimation of a spectral density at a fixed frequency, e.g. at frequency Λ = 0, our procedure allows to perform nonparametric spectral estimation with variable window width which adapts to the smoothness of the true underlying density.     

Comparison of spectral sensitivity using heterochromatic flicker photometry and an acuity criterion

The CIE luminosity function V_δ is based largely upon the spectral sensitivity of normal observers measured by flicker photometry. Nonetheless, it is used to specify illumination for visual tasks in which the performance criterion is not temporal resolution, e.g., acuity tasks. It has recently become clear that different channels in the human visual system detect acuity targets than detect flicker. Furthermore, the flicker and acuity channels have ostensibly different spectral sensitivities. Thus it becomes important to verify that lights equated by a flicker criterion and lights equated by an acuity criterion agree. If the spectral sensitivity measured by flicker and acuity criteria differ, then performance on an acuity task for lights of equal luminance but dissimilar spectral composition will differ. Six monochromatic background fields (460, 500, 550, 580, 600, and 660 nm) were flickermatched to a standard white field. the monochromaticplus-white-standard fields were used as backgrounds for 10 cycle/degree monochromatic gratings presented as increments. Four observers participated in the experiment. Excepting the 460 nm condition, the contrast required to detect a grating on flicker-matched backgrounds is independent of wavelength. Although subserved by different channels, flicker photometric and threshold acuity criteria produce similar spectral sensitivities.     

Validation of continuous-time models with delay

This article is a continuation of an earlier work by Huang [2000. Multivariate model validation in the presence of timevariant disturbance dynamics. Chemical Engineering Science 55, 4583-4595] for validation of discrete time models. We present validation method for continuous-time transfer models with time delay. The proposed procedure is based on the local approach for change detection of model parameters. Both single input single output (SISO) and multiple input multiple output (MIMO) models are considered. The special feature of the proposed algorithm is its ability to detect and isolate changes in the time delay as well as in other parameters. The performance of the proposed method is demonstrated using Monte-Carlo simulations and by application to experimental data from a laboratory scale process.     

On the complex poisson's ratio of a urethane rubber compound

The complex Poisson's ratio of a urethane rubber compound was determined for frequencies up to 700 cps. It is shown that the assumption made by earlier workers using this material, that Poisson's ratio is a numerical constant slightly less than 1/2, while approximately correct at low (creep) frequencies is definitely invalid in certain more elevated frequency bands.     

Poission search models and the evaluation of stopping rules

Mathematically convenient models for a search can be based on a prior representation of the hidden objects and their values by a mixture of Poisson processes. In simple cases, we can find the corresponding Bayes procedures to maximise expected net gains, allowing for the cost of searching. More generally, optimal stopping rules for the search axe difficult to construct and evaluate. We also investigate a procedure based on the asymptotic behaviour of the system when the number of hidden objects is large. This is shown to provide a reasonably effective stopping rule over a wide range of conditions.     

Simulation of Real Discrete Time Gaussian Multivariate Stationary Processes with Given Spectral Densities

In this article we establish a simulation procedure to generate values for a real discrete time multivariate stationary process, based on a factor of spectral density matrix. We prove the convergence of the simulator, at each time epoch, to the actual process, and provide the corresponding rate of convergence. We merely assume that the spectral density matrix is continuous and of bounded variation. By using the positive root factor, we provide an extended version for the Sun and Chaika ( 1997 ) simulator, for real univariate stationary processes.     

CONSISTENT ESTIMATION OF THE FOURTH-ORDER CUMULANT SPECTRAL DENSITY

Abstract. In this paper we consider the estimation of the fourth-order cumulant spectral density. Indeed this is the first case where the cumulant depends on lower-order product moments for a mean-zero stationary process. The proposed estimator of the fourth-order cumulant spectral density is constructed by replacing product moments with appropriately weighted estimates of product moments according to the definition of the fourth-order cumulant spectral density. Asymptotic unbiasedness and consistency are shown to hold for these estimators under stationarity and absolute summability of cumulants up to various orders with no restrictions on the frequencies. An expression for the asymptotic variance is also obtained.     

Interpretation of the Infrared Spectra of Fused Silica

A vibrational analysis was performed for fused silica assuming short-range order in the glassy network. This order is described by an average structural unit based on the model α-quartz. The analysis uses a group theoretical method and the Wilson FG-matrix techniques to predict 16 normal mode vibrational frequencies based on a diagonal force field. The most probable values of the force constants, which were obtained from the best fit between the calculated vibrational frequencies and the measured spectral values, are:

Although the selection rules are not adhered to, 15 predicted frequencies are within the ranges of the spectra of fused silica reported in the literature.     

A colorizer for use in determining an optimal ophthalmic tint

A colorizer for use in the provision of an ophthalmic tint is described. The design differs from that of an earlier model in that the spectral power distribution of the light in the instrument is very similar to the spectral power distribution obtained when tinted glasses are worn under typical lighting. The similarity in spectral power is obtained notwithstanding the fact that the instrument uses an additive mixture of filtered light, whereas tinted lenses use a subtractive mixture of dyes. The precision of color selection is high, and this precision is shown to be necessary to optimize reading fluency. Because of the similarity in spectral power distribution, it is possible to examine the effect of ophthalmic tints not only on reading fluency, but also on the perception and naming of colored surfaces, and the examination can be undertaken by patients who have color vision anomalies. Compared with the earlier design, the use of a diffuse source and seven colored filters reduces the requirement for precision in alignment of components; the variation in color from one instrument to another is, therefore, small, allowing a single calibration for all instruments. This calibration permits the matching of colored ophthalmic lenses to a given colorizer setting, using a computer algorithm which enables practitioners with color vision deficiencies to undertake ophthalmic colorimetry. © 2001 John Wiley & Sons, Inc. Col Res Appl, 26, 246–253, 2001     

A UNIFIED APPROACH TO CONFIDENCE BOUNDS FOR THE AUTOREGRESSIVE SPECTRAL ESTIMATOR

Abstract. Confidence bounds for the spectral density of a stationary time series are derived. A unified method begins with the autoregressive spectral estimate and produces both confidence intervals at single frequencies chosen a priori and a simultaneous confidence band for multiple a posteriori comparisons. The crux is optimization of a quadratic form subject to the constraint imposed by the F -statistic. An approximate method that may produce tighter bounds is described. The former methods are demonstrated on the Waldmeier annual mean sunspot numbers.     

IR studies on preoxidized PAN fibres

IR absorption spectra of preoxidized PAN fibres have been studied in the spectral region 2–15 μ. Observed frequencies have been assigned to the different modes of vibration. The neighbouring frequencies appearing in the stretching mode region of the nitrile group has been interpreted in terms of Fermi-resonance and a basis for the correlation between their intensity ratio and the degree of oxidation has also been discussed.