Extrapolation Interval Research Articles

Independent Wind Power Installations with Optimum Control Being the Part of Wind Power Plant

Based on the analysis of the independent wind power unit control with advanced blade installation to the required angle in accordance with pitch drive motor turn-on time estimation and taking into account the parameters of inductive resistance x1, reduced inductive resistance x′2, active resistance of the stator winding phase r1, reduced active resistance of the winding phase stator r′2, aimed at minimizing the time of the phase voltage transient regulation of the wind turbine generator, so as to improve the quality of the self-excitation process and the performance of power supply under conditions of incomplete information about wind speed and electrical load characteristics that change significantly over time - a criterion for delimiting the access time has been developed for the device to change blade position in terms of proposed and main methodsto develop controlling actions. Access time differentiation is made for the effective matching of the offered and basic ways of wind power installation control blade position, and minimization of time extrapolation interval of wind stream and electric loading promotes wind speed accuracy estimation and power consumption due to steady average values of meteorological and electric and power process, and also provides control time reduction of target control parameters from an existing basic control method, that essentially reduces its participation in decision making process as the given way generates control actions with delay that leads to fluctuations of phase voltage. The software control module of independent wind unit operationwithin the structure of wind power plant with the set advanced time and taking dynamic properties of the system into account that increases voltage stability of modern wind generators for an independent operation mode is developed. The software package for controlling a wind power plant has been improved based on the power unit operation mode - an independent process of electricity generation or for the power system.

The spectral‐voltage calibration technology of multispectral pyrometers based on Gauss–Newton‐genetic algorithm method for nonsource temperature regions

AbstractTo improve the accuracy of the nonsource temperature calibration method, a new method based on a Gauss–Newton‐genetic algorithm (GN‐GA) for the nonsource calibration of a multispectral pyrometer is proposed. Based on Planck's law, a temperature–voltage power function model was established based on constraint optimization, and the temperature–voltage function relationship of each spectral channel was obtained using a GN‐GA algorithm. When the GN‐GA algorithm extrapolated at 1000°C with 3000°C as the starting point, theoretical simulation results showed that, compared with the derivative least squares method, when the wavelengths were 0.4, 0.6, 0.8, and 1.0 μm, the extrapolation accuracy increased by 54.35%, 63.96%, 51.99%, and 44.05%, respectively. The black‐body experiment results showed that this method was feasible in multispectral, pyrometer, extrapolation, temperature–calibration technology. Compared with the results obtained by the derivative least squares method, the accuracy was improved for a given extrapolation temperature region, and the extrapolation interval was longer under the same accuracy.

Application of Approximation Constructions with a Small Number of Parameters for the Estimation of a Rayleigh Fading Multipath Channel with Doppler Spectrum Spreading.

In this article, an algorithm for joint estimation of communication channel gains and signal distortions in a direct conversion receiver is proposed. The received signal model uses approximations with a small number of parameters to reduce the computational complexity of the resulting algorithm. The estimation algorithm is obtained under the assumption of a priori uncertainty about the characteristics of the communication channel and noise distribution using the linear least squares method. Estimation is performed first by the test sequence, then by the information symbols obtained after detection. In addition, an analysis of the noise immunity of quadrature amplitude modulation (QAM) signal reception is carried out using different approximating structures in the estimation algorithm for systems with a single transmitting and receiving antenna (SISO) and for systems with multiple transmitting and receiving antennas (MIMO). Furthermore, this article examines the influence of the duration of the test signal, the number of sessions of its transmission, and the channel extrapolation interval on the quality of signal reception.

A global end-member approach to derive <i>a</i><sub>CDOM</sub>(440) from near-surface optical measurements

Abstract. This study establishes an optical inversion scheme for deriving the absorption coefficient of colored (or chromophoric, depending on the literature) dissolved organic material (CDOM) at the 440 nm wavelength, which can be applied to global water masses with near-equal efficacy. The approach uses a ratio of diffuse attenuation coefficient spectral end-members, i.e., a short- and long-wavelength pair. The global perspective is established by sampling “extremely” clear water plus a generalized extent in turbidity and optical properties that each span 3 decades of dynamic range. A unique data set was collected in oceanic, coastal, and inland waters (as shallow as 0.6 m) from the North Pacific Ocean, the Arctic Ocean, Hawaii, Japan, Puerto Rico, and the western coast of the United States. The data were partitioned using subjective categorizations to define a validation quality subset of conservative water masses (i.e., the inflow and outflow of properties constrain the range in the gradient of a constituent) plus 15 subcategories of more complex water masses that were not necessarily evolving conservatively. The dependence on optical complexity was confirmed with an objective methodology based on a cluster analysis technique. The latter defined five distinct classes with validation quality data present in all classes, but which also decreased in percent composition as a function of increasing class number and optical complexity. Four algorithms based on different validation quality end-members were validated with accuracies of 1.2 %–6.2 %, wherein pairs with the largest spectral span were most accurate. Although algorithm accuracy decreased with the inclusion of more subcategories containing nonconservative water masses, changes to the algorithm fit were small when a preponderance of subcategories were included. The high accuracy for all end-member algorithms was the result of data acquisition and data processing improvements, e.g., increased vertical sampling resolution to less than 1 mm (with pressure transducer precision of 0.03–0.08 mm) and a boundary constraint to mitigate wave-focusing effects, respectively. An independent evaluation with a historical database confirmed the consistency of the algorithmic approach and its application to quality assurance, e.g., to flag data outside expected ranges, identify suspect spectra, and objectively determine the in-water extrapolation interval by converging agreement for all applicable end-member algorithms. The legacy data exhibit degraded performance (as 44 % uncertainty) due to a lack of high-quality near-surface observations, especially for clear waters wherein wave-focusing effects are problematic. The novel optical approach allows the in situ estimation of an in-water constituent in keeping with the accuracy obtained in the laboratory.

Indirect Determination of Vapor Pressures by Capillary Gas–Liquid Chromatography: Analysis of the Reference Vapor-Pressure Data and Their Treatment

Knowledge of low vapor pressures p0 is indispensible for modeling the fate of chemicals in the environment as well as for other important applications. The indirect determination of vapor pressures by the capillary gas–liquid chromatography–relative retention time (GLC–RT) technique has attracted the attention of many research groups, and two review papers devoted to this topic have already been published. To complement these reviews, the quality of the literature vapor pressures for reference compounds is analyzed, along with the influence of the equations used for the temperature dependence of p0 and the effects of the extrapolation interval applied. Since the GLC–RT techniques yield p0 of subcooled liquid even in the case of solid samples, different approaches employed for the recalculation of solid vapor pressures for reference compounds to the values for subcooled liquids are discussed. It is shown that a selection and/or application of the physicochemical properties of the reference compounds can si...

Analysis and short-time extrapolation of stock market indexes through projection onto discrete wavelet subspaces

We consider the problem of short-time extrapolation of blue chips’ stocks indexes in the context of wavelet subspaces following the theory proposed by X.-G. Xia and co-workers in a series of articles [10–13]. The idea is first to approximate the oscillations of the corresponding stock index at some scale by means of the scaling function which is part of a given multi-resolution analysis of L 2 ( R ) . Then, since oscillations at a finer scale are discarded, it becomes possible to extend such a signal up to a certain time in the future; the finer the approximation, the shorter this extrapolation interval. At the numerical level, a so-called Generalized Gerchberg–Papoulis (GGP) algorithm is set up which is shown to converge toward the minimum L 2 norm solution of the extrapolation problem. When it comes to implementation, an acceleration by means of a Conjugate Gradient (CG) routine is necessary in order to obtain quickly a satisfying accuracy. Several examples are investigated with different international stock market indexes.

Numerical prediction methods for clock deviation based on two-way satellite time and frequency transfer data

Three functional models, polynomial, spectral analysis, and modified AR model, are studied and compared in fitting and predicting clock deviation based on the data sequence derived from two-way satellite time and frequency transfer. A robust equivalent weight is applied, which controls the significant influence of outlying observations. Some conclusions show that the prediction precision of robust estimation is better than that of LS. The prediction precision calculated from smoothed observations is higher than that calculated from sampling observations. As a count of the obvious period variations in the clock deviation sequence, the predicted values of polynomial model are implausible. The prediction precision of spectral analysis model is very low, but the principal periods can be determined. The prediction RMS of 6-hour extrapolation interval is 1 ns or so, when modified AR model is used.

Thermal emissivity of coated glazing—simulation versus measurements

Abstract A large variety of coated glazing products are available on the market today. These are used in energy efficient low emissivity (low-e) or solar control windows. Not only the solar optical properties, but also the thermal emissivity of these coated glazing materials are of importance for the performance of such energy efficient windows. The thermal emissivity is calculated from the IR reflectance. A problem is that for accurate determination of the emissivity according to international standards, the reflectance needs to be known between 2000 and 200 cm −1 , and many FTIR spectrophotometers cannot measure below 400 cm −1 . In this paper some different strategies for the extrapolation to 200 cm −1 are discussed. A sensitivity analysis for different types of materials is presented for a few different extrapolation algorithms. The simplest extrapolation procedure assumes a constant reflectance value throughout the extrapolation interval. This appears to work well for surfaces with high reflectance values. A procedure based on a linear relation between the values at a starting wavelength and at the end point of the extrapolation interval or one using a simple second-degree polynomial function can be used when coatings on glass having medium or low reflectance values are evaluated. A guide on how to extrapolate the spectra, according to the different strategies, is included in the Appendix.

Experimental grain size-sensitive flow of hot-pressed Brazilian quartz aggregates

Grain size-sensitive flow may be of particular importance in the flow of rocks in natural high-strain zones. Hot-pressed aggregates of synthetic, ultrafine-grained Brazilian quartz of nominal grain sizes 0.4, 1.3 and 4.5 μm were deformed at 300 MPa confining pressure and temperatures of 1273–1473 K. Fully ductile flow at differential stresses below 200 MPa followed ϵ ̇ =0.4σ exp(−220000/ RT)/d 2 where ϵ ̇ is strain rate (s −1), σ is stress (MPa), d is grain size (microns) and R is the gas constant. Grains remained equant and mostly dislocation-free, without significant crystallographic fabric. Water pressure (∼25–50 MPa) was estimated from water adsorbed onto grain boundaries during specimen fabrication. Flow was inferred to be controlled by silicon volume diffusion and to be sensitive to water fugacity. At differential stresses >200 MPa non-linear flow involved dislocation motion. Extrapolation to natural strain rates and temperatures that predict grain-size sensitive flow in quartz should only be important at >800 K and very small grain sizes (∼1 μm). Flow law parameters may change over the extrapolation interval, e.g. through a transition to control by silicon grain-boundary diffusion, but geological evidence suggests that flow of even very fine-grained quartzites commonly occurs by recrystallization-accommodated dislocation creep, rather than by diffusional accommodation.

Experimental intracrystalline plastic flow in hot-pressed synthetic quartzite prepared from Brazilian quartz crystals

Samples of synthetic, ultrafine-grained quartzite were prepared by hot-pressing aggregates of crushed, clear Brazilian quartz of mean grain size 0.4 μm at 300 MPa and 1373 and 1473 K. The samples displayed rapid grain-growth to ca. 12–20 μm with <2% porosity at 1473 K, facilitated by the 0.6 wt% of water adsorbed onto the grain boundaries during sample preparation. This water could be driven off by pre-heating, thereby preventing grain-growth. Sufficient water was incorporated during growth into the coarsened samples to render them weak and ductile. These were deformed experimentally in the β-quartz field using an argon gas medium apparatus at 300 MPa confining pressure at temperatures mainly between T=1273 and 1473 K. Ductile flow was described by the flow law: ϵ ̇ =10 −4.93σ 2.97f( H 2 O) exp(−242000/ RT) with stress, σ, in MPa, and grain size, d, in microns and strain rate ϵ ̇ in s −1. R is the gas constant and f(H 2O) is water fugacity. Based on observation of grain flattening, optical strain features, shapes and densities of dislocation arrays, and flow law parameters, samples deformed dominantly by dislocation creep, with some contribution from grain-boundary sliding. Bearing in mind possible changes in the flow law parameters over the extrapolation interval and possible effects of the α– β phase transition, extrapolation to natural strain rates and temperatures predicts plastic flow at higher flow stresses at the same water fugacity at greenschist facies temperatures than previously published flow laws.

Robust extrapolation designs for biased polynomial models

Abstract In this article we consider the construction of optimal designs for extrapolation in the polynomial regression setup, allowing for imprecision in the specification of the response function. We adopt a minimax approach, which determines an optimal design to minimize the maximum value of the integrated mean-squared prediction error (IMSPE), with the maximum being evaluated over the departures from the model. It turns out that in straight-line and quadratic regression, the minimax extrapolation designs are the same as the minimum integrated variance (MIV) extrapolation designs, which assume that the fitted models are correct. These designs coincide with the D 1 -optimal designs if the extrapolation interval becomes sufficiently large. For cubic polynomial regression, some comparisons of the performance of the proposed designs with uniform and MIV designs are given.

Extended local Rytov Fourier migration method

We develop a novel depth‐migration method termed the extended local Rytov Fourier (ELRF) migration method. It is based on the scalar wave equation and a local application of the Rytov approximation within each extrapolation interval. Wavefields are Fourier transformed back and forth between the frequency‐space and frequency‐wavenumber domains during wavefield extrapolation. The lateral slowness variations are taken into account in the frequency‐space domain. The method is efficient due to the use of a fast Fourier transform algorithm. Under the small angle approximation, the ELRF method leads to the split‐step Fourier (SSF) method that is unconditionally stable. The ELRF method and the extended local Born Fourier (ELBF) method that we previously developed can handle wider propagation angles than the SSF method and account for the phase and amplitude changes due to the lateral variations of slowness, whereas the SSF method only accounts for the phase changes. The stability of the ELRF method is controlled more easily than that of the ELBF method.

Extended local Born Fourier migration method

A migration approach based on a local application of the Born approximation within each extrapolation interval contains a singularity that can make direct application unstable. Previous authors have suggested adding an imaginary part to the vertical wavenumber to eliminate the singularity. However, their method requires that the reference slowness must be the maximum slowness of a given layer; consequently, the slowness perturbations are larger than those when the average slowness is selected as a reference slowness. Therefore, its applicability is limited. We develop an extended local Born Fourier migration method that circumvents the singularity problem of the local Born solution and makes it possible to choose the average slowness as a reference slowness. It is computationally efficient because of the use of a fast Fourier transform algorithm. It can handle wider angles (or steeper interfaces) and scattering effects of heterogeneities more accurately than the split‐step Fourier (SSF) method, which accounts for only the phase change as a result of the slowness perturbations but not amplitude change. To handle large lateral slowness variations, we introduce different reference slownesses in different regions of a medium to ensure the condition of small perturbation. The migration result obtained using the extended local Born Fourier method with multiple reference slownesses demonstrates that the method can produce high‐quality images of complex structures with large lateral slowness variations.

Unconditionally stable procedure to propagate beams through optical waveguides using the collocation method

The collocation method developed earlier for propagating beams through optical waveguides is unstable for moderately large values of the extrapolation interval. A new procedure is presented to solve the matrix propagation equation in a method that is unconditionally stable for arbitrarily large extrapolation intervals. The new method uses the Fresnel approximation. The numerical performance of the new formulation is compared with that of the original method and with the propagating-beam method.

An improved version of Papoulis-Gerchberg algorithm on band-limited extrapolation

An iterative algorithm for extrapolating analog band-limited signals has been proposed by Papoulis and Gerchberg. <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> By inserting a multiplication by a constant in the above algorithm, chosen to minimize the energy of the error in the extrapolation interval, aconsiderable speed up of its convergence has been achieved.

Optimal estimation for band-limited signals including time domain considerations

The problem of estimation for band-limited signals is investigated. The desired estimate is based on a finite number of time samples taken from a measurement interval of length T M . With no additional information, the estimate must be based on these samples alone. When the signal is band-limited with normalized bandwidth β, this provides additional information which is used to improve the estimate by extrapolating the signal. An extrapolation based on the measured time samples and the known bandwidth is concentrated in time about the measurement interval. The length of this effective extrapolation interval is T_{L} \approx T_{M}/2\beta . Several band-limited estimation methods of this type have been described. A new estimation method for band-limited signals is described which is also based on a time-concentrated extrapolation of the measurements. This new method improves estimates by specifically incorporating the interval T L into the problem formulation and thereby improving the extrapolation on this relevant interval. Estimation error bounds and examples are presented in comparing these two types of band-limited estimation procedures. Estimation with imperfect data is considered. Sensitivity of the band-limited methods to errors in the data is discussed. Estimation with smoothing is utilized in reducing the effects of this noise.

経済的なエクスプリシット時間差分スキームの開発

An economical explicit scheme and its application to a primitive equation model is described. In the present scheme, the low-frequency advection terms are integrated by the leap-frog scheme with a time step interval Δta which is decided by a wind speed of meteorological waves, and not by a gravity wave phase speed. In order to get stable numerical solution, the high frequency gravity wave terms are integrated with a shorter time interval Δtb(≅Δta/M). Time integrations are carried out by combining low frequency terms which are assumed constant during 2Δta leap-frog time extrapolation interval with high frequency terms which are calculated at every Δtb interval. The scheme is three-time-level for low frequency terms. The present scheme is different from the splitting technique proposed by Marchuk (1965).The present economical explicit scheme has the advantage of the easiness in programming and the second order accuracy in the integration of low frequency terms.The present scheme has been applied to the 4L-NHM, operational 4-level northern hemispherical model used in 1978-81 in JMA. The results show that the economical explicit version model produces almost the same prediction as the original (explicit scheme) 4L-NHM. The present scheme saved the computation time as much as the semi-implicit version of 4L-NHM developed by Kudoh (1978) did.