Reply to T. Schneider's comment on "Spatio-temporal filling of missing points in geophysical data sets"

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Spatio-temporal filling of missing points in geophysical data sets

International audienceThe majority of data sets in the geosciences are obtained from observations and measurements of natural systems, rather than in the laboratory. These data sets are often full of gaps, due to to the conditions under which the measurements are made. Missing data give rise to various problems, for example in spectral estimation or in specifying boundary conditions for numerical models. Here we use Singular Spectrum Analysis (SSA) to fill the gaps in several types of data sets. For a univariate record, our procedure uses only temporal correlations in the data to fill in the missing points. For a multivariate record, multi-channel SSA (M-SSA) takes advantage of both spatial and temporal correlations. We iteratively produce estimates of missing data points, which are then used to compute a self-consistent lag-covariance matrix; cross-validation allows us to optimize the window width and number of dominant SSA or M-SSA modes to fill the gaps. The optimal parameters of our procedure depend on the distribution in time (and space) of the missing data, as well as on the variance distribution between oscillatory modes and noise. The algorithm is demonstrated on synthetic examples, as well as on data sets from oceanography, hydrology, atmospheric sciences, and space physics: global sea-surface temperature, flood-water records of the Nile River, the Southern Oscillation Index (SOI), and satellite observations of relativistic electrons

Data-driven PDE discovery with evolutionary approach

The data-driven models allow one to define the model structure in cases when a priori information is not sufficient to build other types of models. The possible way to obtain physical interpretation is the data-driven differential equation discovery techniques. The existing methods of PDE (partial derivative equations) discovery are bound with the sparse regression. However, sparse regression is restricting the resulting model form, since the terms for PDE are defined before regression. The evolutionary approach described in the article has a symbolic regression as the background instead and thus has fewer restrictions on the PDE form. The evolutionary method of PDE discovery (EPDE) is described and tested on several canonical PDEs. The question of robustness is examined on a noised data example

Gap filling of solar wind data by singular spectrum analysis

International audienceObservational data sets in space physics often contain instrumental and sampling errors, as well as large gaps. This is both an obstacle and an incentive for research, since continuous data sets are typically needed for model formulation and validation. For example, the latest global empirical models of Earth's magnetic field are crucial for many space weather applications, and require time-continuous solar wind and interplanetary magnetic field (IMF) data; both of these data sets have large gaps before 1994. Singular spectrum analysis (SSA) reconstructs missing data by using an iteratively inferred, smooth "signal" that captures coherent modes, while "noise" is discarded. In this study, we apply SSA to fill in large gaps in solar wind and IMF data, by combining it with geomagnetic indices that are time-continuous, and generalizing it to multivariate geophysical data consisting of gappy "driver" and continuous "response" records. The reconstruction error estimates provide information on the physics of co-variability between particular solar-wind parameters and geomagnetic indices. Copyright 2010 by the American Geophysical Union

Data-adaptive harmonic spectra and multilayer Stuart-Landau models

Harmonic decompositions of multivariate time series are considered for which we adopt an integral operator approach with periodic semigroup kernels. Spectral decomposition theorems are derived that cover the important cases of two-time statistics drawn from a mixing invariant measure. The corresponding eigenvalues can be grouped per Fourier frequency, and are actually given, at each frequency, as the singular values of a cross-spectral matrix depending on the data. These eigenvalues obey furthermore a variational principle that allows us to define naturally a multidimensional power spectrum. The eigenmodes, as far as they are concerned, exhibit a data-adaptive character manifested in their phase which allows us in turn to define a multidimensional phase spectrum. The resulting data-adaptive harmonic (DAH) modes allow for reducing the data-driven modeling effort to elemental models stacked per frequency, only coupled at different frequencies by the same noise realization. In particular, the DAH decomposition extracts time-dependent coefficients stacked by Fourier frequency which can be efficiently modeled---provided the decay of temporal correlations is sufficiently well-resolved---within a class of multilayer stochastic models (MSMs) tailored here on stochastic Stuart-Landau oscillators. Applications to the Lorenz 96 model and to a stochastic heat equation driven by a space-time white noise, are considered. In both cases, the DAH decomposition allows for an extraction of spatio-temporal modes revealing key features of the dynamics in the embedded phase space. The multilayer Stuart-Landau models (MSLMs) are shown to successfully model the typical patterns of the corresponding time-evolving fields, as well as their statistics of occurrence.Comment: 26 pages, double columns; 15 figure

Improving the processing accuracy of the valve seats of internal combustion engines using diagnostic measurements

© Published under licence by IOP Publishing Ltd. Currently, the main tool of quality management at the enterprises of various industries are statistical methods of quality management. In the literature, mostly on examples of the successful application of control charts for dimensions. More sophisticated measures of quality details not given. The article illustrates a practical application of control charts applied to technologically sophisticated measure of the accuracy of the key indicator affecting the operation of the engine - radial runout of valve seat cylinder head. Data of measurements made in accordance with the standard metrological definitions are processed in the software product "Attestator". As a result, identify the potential percentage of possible marriage, revealed the existence of special reasons to change the values of individual indicators, the index of reproducibility and stability of the process, the decision about the certification process, but the factors of the process that need to be addressed to improve the quality of the products is not revealed. A universal methodology consisting of four steps, the implementation of which allows to develop such a scheme of measurement, which significantly improves the search performance of important technological factors. For example, the same technological operations and the accuracy rate shows the application of the methods. The result of the survey revealed two main factors of the process is bending of the boring bar and the error of the satellite-based suppression will significantly improve the quality of manufacturing of parts

Technique for monitoring the indicators of the total contact spot of spur gears of the truck's differential gear

© Published under licence by IOP Publishing Ltd. The article contains the main provisions of the technique, which allows to control the area of the total contact patch and its position relative to the tooth edges. Graphical schemes for finding indicators are given. An example of the calculation of the indicators established by the methodology, as well as the results of its application for assessing the quality of the setup performance, is considered on the example of processing a differential satellite in the operation of circular gearing

Monte Carlo Simulations of Sexual Reproduction

Modifying the Redfield model of sexual reproduction and the Penna model of biological aging, we compare reproduction with and without recombination in age-structured populations. In contrast to Redfield and in agreement with Bernardes we find sexual reproduction to be preferred to asexual one. In particular, the presence of old but still reproducing males helps the survival of younger females beyond their reproductive age.Comment: 8 pages, plain tex, 7 EPS figures, to appear in PHYSICA

The method of diagnosing machine systems by measuring the accuracy of manufactured parts

© Published under licence by IOP Publishing Ltd. The main provisions of the technique allowing to create a diagnostic complex of the technical state of the machine system, which is informative at the same time of several diagnostic complexes - geometrical accuracy, strain gauge, technological accuracy, the influence of technological heredity - are revealed

Development of the design of a laboratory vibro-grinding machine for preparing samples for metallographic research

© Published under licence by IOP Publishing Ltd. The article presents the results of testing a prototype vibro-grinding laboratory machine for making samples for metallographic examination. The effectiveness of the method and its suitability for the preparation of thin sections during laboratory studies in the discipline "Material Science" have been established