Optimal simultaneous maximum a posterioriestimation of states, noise statistics and parameters I. Algorithm

The simultaneous state and parameter estimation problem for a linear discrete-time system with unknown noise statistics is treated as a large-scale optimization problem. The a posterioriprobability density function is maximized directly with respect to the states and parameters subject to the constraint of the system dynamics. The resulting optimization problem is too large for any of the standard non-linear programming techniques and hence an hierarchical optimization approach is proposed. It turns out that the states can be computed at the first levelfor given noise and system parameters. These, in turn, are to be modified at the second level.The states are to be computed from a large system of linear equations and two solution methods are considered for solving these equations, limiting the horizon to a suitable length. The resulting algorithm is a filter-smoother, suitable for off-line as well as on-line state estimation for given noise and system parameters. The second level problem is split up into two, one for modifying the noise statistics and the other for modifying the system parameters. An adaptive relaxation technique is proposed for modifying the noise statistics and a modified Gauss-Newton technique is used to adjust the system parameters.

Optimal simultaneous maximum a posterioriestimation of states, noise statistics and parameters II. Numerical performance

A very general and numerically quite robust algorithm has been proposed by Sastry and Gauvrit (1980) for system identification. The present paper takes it up and examines its performance on a real test example. The example considered is the lateral dynamics of an aircraft. This is used as a vehicle for demonstrating the performance of various aspects of the algorithm in several possible modes.

Effect of soil variability on the bearing capacity of clay and in slope stability problems

Site-specific geotechnical data are always random and variable in space. In the present study, a procedure for quantifying the variability in geotechnical characterization and design parameters is discussed using the site-specific cone tip resistance data (qc) obtained from static cone penetration test (SCPT). The parameters for the spatial variability modeling of geotechnical parameters i.e. (i) existing trend function in the in situ qc data; (ii) second moment statistics i.e. analysis of mean, variance, and auto-correlation structure of the soil strength and stiffness parameters; and (iii) inputs from the spatial correlation analysis, are utilized in the numerical modeling procedures using the finite difference numerical code FLAC 5.0. The influence of consideration of spatially variable soil parameters on the reliability-based geotechnical deign is studied for the two cases i.e. (a) bearing capacity analysis of a shallow foundation resting on a clayey soil, and (b) analysis of stability and deformation pattern of a cohesive-frictional soil slope. The study highlights the procedure for conducting a site-specific study using field test data such as SCPT in geotechnical analysis and demonstrates that a few additional computations involving soil variability provide a better insight into the role of variability in designs.

Gust Response of Rotor and Propeller Systems

The influence of nonstationary turbulence on rotor and propeller systems is discussed. The review is made from a common analytical basis of nonstationary approach, with emphasis on concepts rather than on details. The necessity of such an approach and its feasibility for predicting a complete set of gust and response statistics together with correlations with somewhat limited test data are appraised.

Random matrices: Universality of ESDs and the circular law

Given an n x n complex matrix A, let mu(A)(x, y) := 1/n vertical bar{1 <= i <= n, Re lambda(i) <= x, Im lambda(i) <= y}vertical bar be the empirical spectral distribution (ESD) of its eigenvalues lambda(i) is an element of C, i = l, ... , n. We consider the limiting distribution (both in probability and in the almost sure convergence sense) of the normalized ESD mu(1/root n An) of a random matrix A(n) = (a(ij))(1 <= i, j <= n), where the random variables a(ij) - E(a(ij)) are i.i.d. copies of a fixed random variable x with unit variance. We prove a universality principle for such ensembles, namely, that the limit distribution in question is independent of the actual choice of x. In particular, in order to compute this distribution, one can assume that x is real or complex Gaussian. As a related result, we show how laws for this ESD follow from laws for the singular value distribution of 1/root n A(n) - zI for complex z. As a corollary, we establish the circular law conjecture (both almost surely and in probability), which asserts that mu(1/root n An) converges to the uniform measure on the unit disc when the a(ij) have zero mean.

Sensitive high-resolution ion microprobe U-Pb dating of prograde and retrograde ultrahigh-temperature metamorphism as exemplified by Sri Lankan granulites

Ultrahigh-temperature (UHT) granulites of the central Highland Complex, Sri Lanka, underwent some of the highest known peak temperatures of crustal metamorphism. Zircon and monazite U-Pb systems in granulites near Kandy, the highest grade region (similar to 1050 degrees C; 0.9 GPa), preserve both a record of the timing of prograde and retrograde phases of UHT metamorphism and evidence for the ages of older protolith components. Zircon grains from a quartz-saturated granulite containing relics of the peak UHT assemblage have remnant detrital cores with dates of ca. 2.5-0.83 Ga. Date clusters of ca. 1.7 and 1.04-0.83 Ga record episodes of zircon growth in the source region of the protolith sediment. Two generations of overgrowths with contrasting Th/U record metamorphic zircon growth at 569 +/- 5 and 551 +/- 7 Ma, probably in the absence and presence of monazite, respectively. The age of coexisting metamorphic monazite (547 +/- 7 Ma) is indistinguishable from that of the younger, low-Th/U zircon overgrowths. Zircon from a quartz-undersaturated monazite-absent UHT granulite with a mainly retrograde assemblage is mostly metamorphic (551 +/- 5 Ma). The ca. 570 Ma zircon overgrowths in the quartz-saturated granulite probably record partial melting just before or at the metamorphic peak. The ca. 550 Ma zircon in both rocks, and the ca. 550 Ma monazite in the quartz-saturated sample, record post-peak isothermal decompression. A possible model for this pressure-temperature-time evolution is ultrahot collisional orogeny during the assembly of Gondwana, locally superheated by basaltic underplating, followed by fast extensional exhumation.

Electron transfer statistics and thermal fluctuations in molecular junctions

We derive analytical expressions for probability distribution function (PDF) for electron transport in a simple model of quantum junction in presence of thermal fluctuations. Our approach is based on the large deviation theory combined with the generating function method. For large number of electrons transferred, the PDF is found to decay exponentially in the tails with different rates due to applied bias. This asymmetry in the PDF is related to the fluctuation theorem. Statistics of fluctuations are analyzed in terms of the Fano factor. Thermal fluctuations play a quantitative role in determining the statistics of electron transfer; they tend to suppress the average current while enhancing the fluctuations in particle transfer. This gives rise to both bunching and antibunching phenomena as determined by the Fano factor. The thermal fluctuations and shot noise compete with each other and determine the net (effective) statistics of particle transfer. Exact analytical expression is obtained for delay time distribution. The optimal values of the delay time between successive electron transfers can be lowered below the corresponding shot noise values by tuning the thermal effects. (C) 2015 AIP Publishing LLC.