Models for vector multicomponent physical quantities and a multivariate test method for optical measurement systems

Models are presented for vector multicomponent physical quantities that are adapted for algorithmic structure synthesis of optical measuring systems on the basis of a multivariate test method. Realization examples are given. __________ Translated from Izmeritel’naya Tekhnika, No. 12, pp. 10–13, December, 2006.     

New methods and technologies for the identification of optical measurements performed by video cameras with degeneration in the arrangement of test objects in the plane

New methods and technologies for the identification of optical measurements for video cameras in cases where the spatial arrangement of the test objects (test objects) in the plane becomes degenerate are considered. Moscow, Russia. Translated from Izmeritel’naya Tekhnika, No. 5, pp. 23–29, May, 2008.     

Statistical monitoring of over-dispersed multivariate count data using approximate likelihood ratio tests

In this paper, we develop a statistical monitoring scheme for multivariate count data. In many applications involving multivariate count data, individual variables are not only correlated to each other, but also over-dispersed. Traditional statistical monitoring methods for multivariate count data that assume simple statistical models fail to fit the data collected when the underlying process is under normal working state, also referred to as the in-control state. Therefore, we propose a monitoring scheme which is based on the Poisson–multivariate Gaussian mixed model. Although such models are quite flexible, efficient statistical monitoring schemes for such models have not been developed. In this paper, we develop likelihood ratio test-based monitoring schemes that are shown to be superior to standard multivariate statistical monitoring schemes. The key challenge in developing likelihood ratio test for the Poisson–multivariate Gaussian mixed models is that the likelihood function can only be calculated by multidimensional numerical integration. We tackle this issue using an approximation of this complex likelihood function.     

On the optimal scheduling of periodic tests and maintenance for reliable redundant components

Periodically, some m of the n redundant components of a dependable system may have to be taken out of service for inspection, testing or preventive maintenance. The system is then constrained to operate with lower (n−m) redundancy and thus with less reliability during these periods. However, more frequent periodic inspections decrease the probability that a component fail undetected in the time interval between successive inspections. An optimal time schedule of periodic preventive operations arises from these two conflicting factors, balancing the loss of redundancy during inspections against the reliability benefits of more frequent inspections.Considering no other factor than this decreased redundancy at inspection time, this paper demonstrates the existence of an optimal interval between inspections, which maximizes the mean time between system failures. By suitable transformations and variable identifications, an analytic closed form expression of the optimum is obtained for the general (m, n) case. The optimum is shown to be unique within the ranges of parameter values valid in practice; its expression is easy to evaluate and shown to be useful to analyze and understand the influence of these parameters.Inspections are assumed to be perfect, i.e. they cause no component failure by themselves and leave no failure undetected. In this sense, the optimum determines a lowest bound for the system failure rate that can be achieved by a system of n-redundant components, m of which require for inspection or maintenance recurrent periods of unavailability of length t.The model and its general closed form solution are believed to be new [2] and [5]. Previous work [1], [4] and [10] had computed optimal values for an estimation of a time average of system unavailability, but by numerical procedures only and with different numerical approximations, other objectives and model assumptions (one component only inspected at a time), and taking into account failures caused by testing itself, repair and demands (see in particular [6], [7] and [9]).System properties and practical implications are derived from the closed form analytical expression. Possible extensions of the model are discussed. The model has been applied to the scheduling of the periodic tests of nuclear reactor protection systems.     

Nonparametric tests and the stationarity of signal amplitude and time measurements

Nonparametric tests have been applied to the stationarity of measurements for pulse edge length measurements, with the object of determining the time taken for a stroboscopic oscilloscope to transfer from the dynamic mode to the static one. Translated from Izmeritel'naya Tekhnika, No. 11, pp. 3–6, November, 2008.     

Quantitative comparison of tympanic membrane displacements using two optical methods to recover the optical phase

The study and quantification of the tympanic membrane (TM) displacements add important information to advance the knowledge about the hearing process. A comparative statistical analysis between two commonly used demodulation methods employed to recover the optical phase in digital holographic interferometry, namely the fast Fourier transform and phase-shifting interferometry, is presented as applied to study thin tissues such as the TM. The resulting experimental TM surface displacement data are used to contrast both methods through the analysis of variance and F tests. Data are gathered when the TMs are excited with continuous sound stimuli at levels 86, 89 and 93 dB SPL for the frequencies of 800, 1300 and 2500 Hz under the same experimental conditions. The statistical analysis shows repeatability in z-direction displacements with a standard deviation of 0.086, 0.098 and 0.080 μm using the Fourier method, and 0.080, 0.104 and 0.055 μm with the phase-shifting method at a 95% confidence level for all frequencies. The precision and accuracy are evaluated by means of the coefficient of variation; the results with the Fourier method are 0.06143, 0.06125, 0.06154 and 0.06154, 0.06118, 0.06111 with phase-shifting. The relative error between both methods is 7.143, 6.250 and 30.769%. On comparing the measured displacements, the results indicate that there is no statistically significant difference between both methods for frequencies at 800 and 1300 Hz; however, errors and other statistics increase at 2500 Hz.     

New capability indices for evaluating the performance of multivariate manufacturing processes

Generally, an industrial product has more than one quality characteristic. In order to establish performance measures for evaluating the capability of a multivariate manufacturing process, several multivariate process capability indices have been developed in the past few years. Among them, Taam's MC_p and MC_pm indices have the drawback of overestimation and Hubele's three‐component capability vector lacks simplicity in practice. In this article, taking the correlation among multiple quality characteristics into account, we develop two novel indices; NMC_p and NMC_pm. Using two numerical examples we demonstrate that the true performance of multivariate processes are accurately reflected in our NMC_p and NMC_pm indices and in their associated interval estimates. Finally, simulation results show that our indices outperform both those of Taam and Hubele. Copyright © 2009 John Wiley & Sons, Ltd.     

The influence of crystallographic orientation on crack tip displacements of microstructurally small, kinked crack crossing the grain boundary

The paper presents an analysis of the effects of grain orientations on a short, kinked surface crack in a 316L stainless steel. The kinking of the crack is assumed to take place at the boundary between two neighbouring grains. The analysis is based on a plane-strain finite element crystal plasticity model. The model consists of 212 randomly shaped, sized and oriented grains, loaded monotonically in uniaxial tension to a maximum load of 0.96R_p0.2 (240 MPa). The influence that a random grain structure imposes on a Stage I crack is assessed by calculating the crack tip opening (CTOD) displacements for bicrystal as well as for polycrystal models, considering different crystallographic orientations. Since a Stage I crack is assumed, the crack is always placed in a slip plane. Results from a bicrystal case show that the maximal CTODs are directly related to the stiffness of the grain containing the crack extension. Anisotropic elasticity and crystal plasticity both contribute to this grain stiffness, resulting in maximal CTOD when Schmid factors are the highest on two slip planes. Such crystallographic orientation results in a soft elasto-plastic response. Anisotropic elasticity can additionally increase the softness of a grain at certain crystallographic orientations. Minimal anisotropic elasticity at the crystallographic orientations with the highest Schmid factors causes the CTOD to be maximized. Presuming that the crack will preferably follow the slip plane where the crack tip opening displacement is highest, we show that the crystallographic orientation can affect the CTOD values by a factor of up to 7.7. For a given grain orientation the maximum CTOD is attained when the crack extension deflection into a second grain is between −75.141° and 34°. For the polycrystal case we show that grains beyond the first two crack-containing grains change the CTOD by a factor of up to 3.3 and that the largest CTODs are obtained when placing the crack into a slip plane with crack extension that results in a crack extension being more perpendicular to the external load.     

Theoretical analysis of hollow ring-core optical fibre for transmitting orbital angular momentum modes

Ring-core optical fibre has been successfully demonstrated to have good performance for lifting mode degeneracy, and maintaining orbital angular momentum (OAM) modes in the first radial order, making it promising for applications of OAM mode multiplexing and generation of cylindrical vector beams. The degeneracy lift can be intensified using a hollow ring-core fibre, i.e. when the innermost layer of waveguide is air. The cut-off ring thickness for supporting the lowest OAM modes in radial order are obtained under various refractive index differences between the transport layer and the cladding. To optimize the design, our analysis addresses the dependence of modal properties on the fibre structure parameters, such as the effective area (A_eff) of respective OAM mode, and the differential mode delay.     

Structural,optical and magnetic properties of the Fe2TiO5 nanopowders

Iron titanate nanopowders with a particle size range of 48–70?nm could be obtained after calcinations of the dried gel at 900°C for 2?h. Fe₂TiO₅ indicates a ferrimagnetic–paramagnetic behaviour, as evidenced by using vibrating sample magnetometer at room temperature. In the temperature range of 25–300°C the empirical equation of the heat capacity C _p (J/mol?K)?=??692.328?+?1.39?T?+?3.757?×?10⁷/T ² for Fe₂TiO₅ was determined from differential scanning calorimetry. Direct optical band gap of Fe₂TiO₅ was calculated using the Tauc model by UV-Vis diffuse reflectance spectroscopy. Band gap energy of Fe₂TiO₅ was determined as 1.95?eV.     

Validation of sobriety tests for the marine environment

The objective of this project was to develop sobriety tests that can be administered in the seated position to assist water patrol officers in detecting alcohol-related impairment in boaters. Four seated sobriety tests were administered to 330 boaters to determine the tests’ usefulness in classifying boaters as having blood alcohol concentrations (BACs) below the illegal limit (BAC < .08%) or above the illegal limit (BAC ≥ .08%). Data were obtained by a team of four marine officers and two civilian observers on Lake of the Ozarks in central Missouri. The overall correct percentages, sensitivity, and specificity of the tests were consistent with what is typically reported in literature on the roadside sobriety tests. The tests’ reliability was also consistent with what is typically reported in literature on the roadside sobriety tests. Thus, the four tests may assist marine officers with assessments of alcohol-related impairment in boaters.     

Solution of a three-dimensional problem of the elasticity theory in terms of displacements for an isotropic elastic layer

A new method is proposed for solving a three-dimensional problem of the elasticity theory for a layer in terms of displacements. It is much easier to satisfy the boundary conditions within the framework of this approach than with the known methods. An example brought to numerical results is considered. __________ Translated from Problemy Prochnosti, No. 3, pp. 38–46, May–June, 2008.     

Sampling of wood for mechanical tests on the basis of density

Two methods are described for sampling wood for mechanical tests on the basis of density. These methods enable matched sets of samples to be defined within a common supply of test materials, or a single set of samples to be matched to a pre-specified density distribution. Examples from the work of the authors are used to illustrate the accuracy of each method. Underlying principles are applicable if another non-destructively evaluated parameter is used as the target property in lieu of density. Research carried out at Timber Research and Development Association, United Kingdom.     

New methods and technologies for processing video images in full-scale tests of complex technical systems

New methods and technologies for processing optical information obtained on the basis of video images in combined full-scale tests of several complex technical systems are considered. It is shown that the best results are achieved with the use of an adaptive procedure that determines the admissible degree of sharpening of the contours of the images. Translated from Izmeritel’naya Tekhnika, No. 4, pp. 20–24, April, 2009