A Novel Sparse Polynomial Expansion Method for Interval and Random Response Analysis of Uncertain Vibro-Acoustic System

For the vibro-acoustic system with interval and random uncertainties, polynomial chaos expansions have received broad and persistent attention. Nevertheless, the cost of the computation process increases sharply with the increasing number of uncertain parameters. This study presents a novel interval and random polynomial expansion method, called Sparse Grids’ Sequential Sampling-based Interval and Random Arbitrary Polynomial Chaos (SGS-IRAPC) method, to obtain the response of a vibro-acoustic system with interval and random uncertainties. The proposed SGS-IRAPC retains the accuracy and the simplicity of the traditional arbitrary polynomial chaos method, while avoiding its inefficiency. In the SGS-IRAPC, the response is approximated by the moment-based arbitrary polynomial chaos expansion and the expansion coefficient is determined by the least squares approximation method. A new sparse sampling scheme combined the sparse grids’ scheme with the sequential sampling scheme which is employed to generate the sampling points used to calculate the expansion coefficient to decrease the computational cost. The efficiency of the proposed surrogate method is demonstrated using a typical mathematical problem and an engineering application.

Monte Carlo transmission line modelling of multilayer optical coatings for performance sensitivity of exoplanet spectroscopy

<p>Multilayer optical coatings are widely used on the surface of optical components to enhance the transmittance of light in certain spectral regions while reducing it in other regions. Discrepancies between the measured and predicted spectral performance of optical components with such coatings can primarily be attributed to deposition errors and uncertainties in the refractive indices of the materials used for these coatings. Our simulation uses two-dimensional transmission line modelling to evaluate the transmittance of light at a given angle of incidence through multilayer coatings deposited on a substrate material. We perform a number of Monte Carlo simulations to obtain statistical information about the tolerance of the coating performance to systematic and random uncertainties in deposition thickness, refractive index and operating temperature. We present the posterior distributions of the deviations from the nominal performance that result from the propagation of each of these uncertainties for a number of hypothetical scenarios. We find that these uncertainties have the potential to cause significant differences between the designed and achieved performance. Our results indicate that the sensitivity of each layer to the various sources of uncertainties can vary on a case-by-case basis. With the aid of accurate manufacturing recipes and uncertainty amplitudes from commercial manufacturers, this simulation can provide a proficient tool to predict variations in the performance of multilayer optical coatings used in exoplanet spectroscopy.</p>

A method for random uncertainties validation and probing the natural variability with application to TROPOMI on board Sentinel-5P total ozone measurements

In this paper, we discuss the method for validation of random uncertainties in the remote sensing measurements based on evaluation of the structure function, i.e., root-mean-square differences as a function of increasing spatiotemporal separation of the measurements. The limit at the zero mismatch provides the experimental estimate of random noise in the data. At the same time, this method allows probing of the natural variability of the measured parameter. As an illustration, we applied this method to the clear-sky total ozone measurements by the TROPOspheric Monitoring Instrument (TROPOMI) on board the Sentinel-5P satellite. We found that the random uncertainties reported by the TROPOMI inversion algorithm, which are in the range 1–2 DU, agree well with the experimental uncertainty estimates by the structure function. Our analysis of the structure function has shown the expected results on total ozone variability: it is significantly smaller in the tropics compared to mid-latitudes. At mid-latitudes, ozone variability is much larger in winter than in summer. The ozone structure function is anisotropic (being larger in the latitudinal direction) at horizontal scales larger than 10–20 km. The structure function rapidly grows with the separation distance. At mid-latitudes in winter, the ozone values can differ by 5 % at separations 300–500 km. The method discussed is a powerful tool in experimental estimates of the random noise in data and studies of natural variability, and it can be used in various applications.

Quantifying Global and Random Uncertainties in High Resolution Global Geomagnetic Field Models Used for Directional Drilling

Summary Total field strength, declination, and dip angle of the Earth's magnetic field, in conjunction with gravity, are used by magnetic-survey tools to determine a wellbore's location. Magnetic field values may be obtained from global models that, depending on the model, have a wide range of spatial resolution at the Earth's surface from large scale (3000 km) to small scale (28 km). The magnetic field varies continuously in both time and space, so no model can fully capture the complexity of all sources; hence, there are uncertainties associated with the values provided. The SPE Wellbore Positioning Technical Section/Industry Steering Committee on Wellbore Surveying Accuracy (ISCWSA) published their original measurement-while-drilling (MWD) error model in 2000. Such models and uncertainties define positional error ellipsoids along the wellbore, which assist the driller in achieving their geological target, in addition to aiding collision avoidance. With the recent update to Revision 5 of the ISCWSA error model, we have reassessed the uncertainties associated with our latest high-resolution global magnetic field model. We describe the derivation of location-specific global and random uncertainties for use with predicted geomagnetic values from high-resolution models within magnetic MWD survey-tool-error models. We propose a sophisticated approach to provide realistic values at different locations around the globe; for example, we determine separate errors for regions where the models have high spatial resolution from aeromagnetic data compared to regions where only satellite data are available. The combined uncertainties are freely available via a web service with which the user can also see how they vary with time. The use of the revised uncertainty values in the MWD-error model, in most cases, reduces the positional error ellipsoids and allows better use of the increased accuracy from recent improvements in geomagnetic modeling. This is demonstrated using the new uncertainty values in the MWD-error model for three standard ISCWSA well profiles. A fourth theoretical well offshore Brazil where the vertical magnetic field is weak shows that with drillstring interference correction relying on the more uncertain magnetic dip, the positional error ellipsoids can increase. This is clearly of concern for attaining geological targets and collision avoidance.

Comparative characterization of different kinds of chromatographic quantification using the double standard addition method

Different algorithms for processing the quantitative gas chromato­gra­­phic ana­lysis data using the double standard addition method are compared for their accuracy. Three principal approaches are possible for such processing: I – simple comparison of values determined by sing­le and double standard additions, II – approximation of «peak area of ana­lyte» (S) – «mass of standard addition» (madd) depen­den­ce by the least squa­res method [linear reg­res­sion, m(S)], and III – independent quantification of analyte with both standard additi­ons follo­wed by the linear extrapolation of two sub-results on the so-cal­led «zero standard addi­tion», mx(madd ® 0). It is concluded that the quantitation results obtained using the various modes of the method are comparable in accuracy, but somewhat underestimated relative to the specified amounts of analytes. The principal reason of such systematic errors is the eva­po­ration of the solvent during the successive injecting of the same samples into the gas chroma­to­graph. Due to this reason the peak are­as, measured after the standard addition, appear to be slight­­ly increased and this leads to the systematic underestimation of the results. The second (less impor­tant) factor is the small increa­se of the samp­le volumes due to the addition of the compo­nents to be determined. It is confirmed that the systematic errors of different modes of standard addition are not exceeding the values of their random uncertainties. The op­ti­mal results (considering their signs of deviations) are provided using the double standard addition method with extrapolation of sub-results on «zero standard addition». In order to exclude the possible influence of «human factor» (increasing the re­sults precision during the series of analyses of similar samples due to the rising experience of analytical chemists) all parallel measurements have been per­for­med by bachelor students of the Chemistry Ins­titute of the St. Petersburg State University in the course of their laboratory practical works in chromatography. Such organization of experiments increases their credibility as it excluded the dependence of the results on the qualification of chemists.

A method for random uncertainties validation and probing the natural variability with application to TROPOMI/Sentinel5P total ozone measurements

In this paper, we discuss the method for validation of random uncertainties in the remote sensing measurements based on evaluation of the structure function, i.e., root-mean-square differences as a function of increasing spatio-temporal separation of the measurements. The limit at the zero mismatch provides the experimental estimate of random noise in the data. At the same time, this method allows probing the natural variability of the measured parameter. As an illustration, we applied this method to the clear-sky total ozone measurements by TROPOMI/Sentinel-5P. We found that the random uncertainties reported by the TROPOMI inversion algorithm, which are in the range 1–2 DU, agree well with the experimental uncertainty estimated by the structure function. Our analysis of the structure function has shown the expected results on total ozone variability: it is significantly smaller in the tropics compared to mid-latitudes. At mid-latitudes, ozone variability is much larger in winter than in summer. The ozone structure function is anisotropic (being larger in latitudinal direction) at horizontal scales larger than 10–20 km. The structure function rapidly grows with the separation distance. At mid-latitudes in winter, the ozone values can differ by 5 % at separations 300–500 km. The discussed method is a powerful tool in experimental estimates of the random noise in data and studies of natural variability and it can be used in various applications.