Stochastic realization approach to the efficient simulation of phase screens

The phase screen method is a well-established approach to take into account the effects of atmospheric turbulence in astronomical seeing. This is of key importance in designing adaptive optics for new-generation telescopes, in particular in view of applications such as exoplanet detection or long-exposure spectroscopy. We present an innovative approach to simulate turbulent phase that is based on stochastic realization theory. The method shows appealing properties in terms of both accuracy in reconstructing the structure function and compactness of the representation.     

Multiscale stochastic simulations for tensile testing of nanotube-based macroscopic cables

Thousands of multiscale stochastic simulations are carried out in order to perform the first in-silico tensile tests of carbon nanotube (CNT)-based macroscopic cables with varying length. The longest treated cable is the space-elevator megacable but more realistic shorter cables are also considered in this bottom-up investigation. Different sizes, shapes, and concentrations of defects are simulated, resulting in cable macrostrengths not larger than approximately 10 GPa, which is much smaller than the theoretical nanotube strength (approximately 100 GPa). No best-fit parameters are present in the multiscale simulations: the input at level 1 is directly estimated from nanotensile tests of CNTs, whereas its output is considered as the input for the level 2, and so on up to level 5, corresponding to the megacable. Thus, five hierarchical levels are used to span lengths from that of a single nanotube (approximately 100 nm) to that of the space-elevator megacable (approximately 100 Mm).     

Statistical properties of finite-bandwidth radiation scattered by random amplitude screens and random phase screens

We investigate the effect of finite bandwidth of the incident radiation on scattering by thin layers that introduce random phase or amplitude variations. In particular, we calculate the scintillation index of the propagating radiation for smoothly varying and fractal phase screens and for random telegraph wave and checkerboard amplitude screens. Increasing the bandwidth of the incident radiation reduces the fluctuations of the scattered intensity over the whole propagation path, except in the case of the smoothly varying phase screen, where geometrical optics features in the pattern persist in the focusing region.     

Multiscale windowed Fourier transform for phase extraction of fringe patterns

A multiscale windowed Fourier transform for phase extraction of fringe patterns is presented. A local stationary length of signal is used to control the window width of a windowed Fourier transform automatically, which is measured by an instantaneous frequency gradient. The instantaneous frequency of the fringe pattern is obtained by detecting the ridge of the wavelet transform. The numerical simulation and experiment have proved the validity of this method. The combination of the windowed Fourier transform and the wavelet transform makes the extracted phase more precise than other methods.     

Multiscale stochastic finite element modeling of random elastic heterogeneous materials

In Xu et al. (Comput Struct 87:1416–1426, 2009) a novel Green-function-based multiscale stochastic finite element method (MSFEM) was proposed to model boundary value problems involving random heterogeneous materials. In this paper, we describe in detail computational aspects of the MSFEM explicitly across macro–meso–micro scales. Different numerical algorithms are introduced and compared in terms of numerical accuracy and convergence.     

基于正交化HHT和随机相位模拟非平稳随机过程

模拟非平稳随机过程已经成为工程中经常遇到的情况,使非平稳过程的大量模拟样本具有相同的统计特性并不容易.基于样本记录正交HHT变换的Hilbert谱提出了非平稳随机过程的模拟方法.首先,利用正交化方法对IMF分量进行处理,避免了传统EMD分解造成的能量泄漏.第二步,把样本的Hilbert谱均值作为随机过程的目标Hilbert谱,通过引入随机相位进行非平稳随机过程的仿真,并且给出了随机过程的统计特性函数.通过对低频地震动记录和高频地铁振动记录的模拟算例表明,模拟的非平稳过程样本与原记录在时频分布上非常接近,具有相同的统计特性.     

基于正交化HHT和随机相位模拟非平稳随机过程

模拟非平稳随机过程已经成为工程中经常遇到的情况,使非平稳过程的大量模拟样本具有相同的统计特性并不容易。基于样本记录正交HHT变换的Hilbert谱提出了非平稳随机过程的模拟方法。首先,利用正交化方法对IMF分量进行处理,避免了传统EMD分解造成的能量泄漏。第二步,把样本的Hilbert谱均值作为随机过程的目标Hilbert谱,通过引入随机相位进行非平稳随机过程的仿真,并且给出了随机过程的统计特性函数。通过对低频地震动记录和高频地铁振动记录的模拟算例表明,模拟的非平稳过程样本与原记录在时频分布上非常接近,具有相同的统计特性。     

Multiscale approach for the design of composite sandwich structures for train application

In the present work a multiscale approach is considered for the design of composite sandwich structures for a roof of railway vehicle. The procedure consists in different steps that start from cost/benefit analysis on materials and their manufacturing process and cycle up to analysis of sub-components and entire structures. Each step is characterized by experimental, theoretical and numerical studies. The design activities herein presented count experimental campaigns able to characterize both the properties of novel sandwich material, manufactured expressly for transportation industry, the sandwich and joint behaviors. Analytical and numerical approaches have been used to validate and optimize the structural layout. Finite element analysis has been also performed on a test article to verify the “new” sandwich roof in regard to structural requirements suggested by European Code.     

Optimization-oriented exponential-polynomial-closure approach for analyzing nonlinear stochastic oscillators

A novel method named optimization-oriented exponential-polynomial-closure approach is proposed in this article. The main idea of this attempt is to extend the original exponential-polynomial-closure solution procedure methodologically by minimizing the resulted residual error square of the governing equation, which is achieved after an exponential polynomial is adopted as the approximate solution. The objective function for computing the parameters in the approximate solutions of nonlinear random oscillators is then formulated. The probabilistic solutions of the oscillators obtained by the presented approach are verified by the exact solutions in some special cases or by Monte Carlo simulation. Numerical examples indicate that the solutions attained by the presented approach match with the exact or Monte Carlo simulation solutions. The advantage of the presented solution procedure is that it can provide a much more accurate solution than the Equivalent Linearization approach and it is much more efficient than Monte Carlo simulation as demonstrated by the numerical examples.     

Implementation of fast-Fourier-transform-based simulations of extra-large atmospheric phase and scintillation screens

Fast-Fourier-transform-based simulations of single-layer atmospheric von Kármán phase screens and Kolmogorov scintillation screens up to hundreds of meters in size were implemented and tested for applications with percent range accuracy. The tests included the expected and the observed structure and pupil variance functions; for the phase, the tests also included the Fried turbulence parameter r0 measured by the seeing and by a simulated differential image motion monitor. The standard compensations used to correct the undersampling at low spatial frequencies were improved, and those needed for the high spatial frequencies were determined analytically. The limiting ratios of the screen sampling step to r0 and of the screen size to the pupil aperture were estimated by means of the simulated data. Sample results are shown that demonstrate the performances of the simulations for single-layer Kolmogorov and von Kármán phase screens up to 200 m in size and for Kolmogorov scintillation screens for pupils up to 50 m of aperture.     

Simulation-based optimisation approach for the stochastic two-echelon logistics problem

This work proposes a simulation-based optimisation approach for the two-echelon vehicle routing problem with stochastic demands (2E-VRPSD). In the proposed 2E-VRPSD, freight delivery from the depot to the customers is managed by shipping the freight through intermediate satellites, while each customer has a stochastic demand. The 2E-VRPSD is an extension of the famous capacitated vehicle routing problem with stochastic demands and the two-echelon vehicle routing problem (2E-VRP). A tabu search algorithm is designed to solve the 2E-VRPSD, in which Monte Carlo sampling is adopted to tackle the issue of stochastic demands. Modified two-echelon vehicle routing problem benchmark instances are used in the numerical experiments. The computational results show the advantage of the proposed simulation-based approach.     

Functional screens for electronic reliability

This paper describes a class of reliability screens for use in the manufacturing process of electronic products which are directly related to the funcationality of the product being produced. The field reliability that was attained from using functional screening on an example product is presented. Because of the exceptionally low failure occurrence now possible in today's products, some simple alternative reliability monitoring statistics based on the binomial are suggested. Implications of this improved reliability on the effectiveness of screening methods is discussed, and the notion of field failures as screening escapes is introduced. Then some reasons to experiment with functional stress screens in place of a total reliance on the more traditional environmental stress screens are presented. Finally, the characteristics of functional screens are presented. Careful experimentation using appropriate statistical analysis in developing and comparing screening approaches is emphasized throughout this paper.     

Neumann enriched polynomial chaos approach for stochastic finite element problems

An enrichment scheme based upon the Neumann expansion method is proposed to augment the deterministic coefficient vectors associated with the polynomial chaos expansion method. The proposed approach relies upon a split of the random variables into two statistically independent sets. The principal variability of the system is captured by propagating a limited number of random variables through a low-ordered polynomial chaos expansion method. The remaining random variables are propagated by a Neumann expansion method. In turn, the random variables associated with the Neumann expansion method are utilised to enrich the polynomial chaos approach. The effect of this enrichment is explicitly captured in a new augmented definition of the coefficients of the polynomial chaos expansion. This approach allows one to consider a larger number of random variables within the scope of spectral stochastic finite element analysis in a computationally efficient manner. Closed-form expressions for the first two response moments are provided. The proposed enrichment method is used to analyse two numerical examples: the bending of a cantilever beam and the flow through porous media. Both systems contain distributed stochastic properties. The results are compared with those obtained using direct Monte Carlo simulations and using the classical polynomial chaos expansion approach.     

Proactive approach for stochastic RCMPSP based on multi-priority rule combinations

Empirical evidence shows that profitability does not always rise when lean management (LM) is implemented. This paper reviews the literature that has empirically analysed how LM impacts financial performance in order to identify the most used assessment model and the direction and significance of the findings. We have found that the most comprehensive models, those considering financial and operational indicators and contextual factors, find a positive and significant impact of LM on financial performance. These findings can benefit managers requiring an assessment of LM and the building of an evaluation system and can serve as a guideline for monitoring LM implementation.     

Agglomerative clustering-based approach for two-dimensional phase unwrapping

We describe a novel algorithm for two-dimensional phase unwrapping. The technique combines the principles of agglomerative clustering and use of heuristics to construct a discontinuous quality-guided path. Unlike other quality-guided algorithms, which establish the path at the start of the unwrapping process, our technique constructs the path as the unwrapping process evolves. This makes the technique less prone to error propagation, although it presents higher execution times than other existing algorithms. The algorithm reacts satisfactorily to random noise and breaks in the phase distribution. A variation of the algorithm is also presented that considerably reduces the execution time without affecting the results significantly.     

Multiscale modelling approach for predicting solidification structure evolution in vacuum arc remelted superalloy ingots

Abstract

The present paper describes the mathematical development and validation of a comprehensive stochastic model capable of predicting at the mesoscopic level the solidification structure, Laves, and NbC phases in superalloy ingots processed by vacuum arc remelting (VAR) technology. The multiscale modelling approach consists of a coupling between a fully transient deterministic macroscopic code and a stochastic mesoscopic solidification structure code. Predictions from the model were validated against experimental measurements. Multiscale model predictions are compared against a commercial size VAR ingot.     

Dot trajectories in the superposition of random screens: analysis and synthesis

Moiré effects that occur in the superposition of aperiodic layers such as correlated random dot screens are known as Glass patterns. One of the most interesting properties of such moiré effects, which clearly distinguish them from their periodic counterparts, is undoubtedly the appearence in the superposition of intriguing microstructure dot alignments, also known as dot trajectories. These dot trajectories may have different geometric shapes, depending on the transformations undergone by the superposed layers. In the case of simple linear transformations such as layer rotations or layer scalings, the resulting dot trajectories are rather simple (circular, radial, spiral, elliptic, hyperbolic, linear, etc.); but in more complex layer transformations the dot trajectories can have much more interesting and surprising shapes. A full mathematical analysis of the dot trajectories, their morphology, and their various properties is provided. Furthermore, it is shown how the approach also allows us to synthesize correlated random screens that give in their superposition dot trajectories having any desired geometric shapes. Finally, it is also explained why such dot trajectories are visible only in superpositions of aperiodic screens but not in superpositions of periodic screens.     

A non-stationary stochastic model for periodic excitation with random phase modulation

The paper presents a non-stationary stochastic model for periodic excitation with random phase modulation, where the phase modulation is modeled as a modulated stationary. Gaussian process. Applications of the model are demonstrated by analysis of response of a single-degree-of-freedom (SDOF) system under such an excitation. The response is, in general, non-Gaussian. Cases of step, rectangular, and exponential envelopes are considered in the present study. The nonstationary second and fourth order moments are calculated by numerically solving the transient moment equations. Non-Gaussianity of the response is studied in terms of the non-stationary excess factor. Some numerical results are presented. The influences of system parameters, build-up and decay rates as well as duration of random phase modulation on the moment response of the SDOF system are discussed.     

Broadband, static wave-front generation: Na-Ag ion-exchange phase screens and telescope emulation

We test the statistical properties of static, atmospherelike wave fronts in glass that allow repeatable testing of astronomical adaptive optics instrumentation. The technology is mask-structured ion exchange (MSI) in glass and has significant advantages over other transmissive technologies. The screens are easy to clean, are insensitive to ambient temperature changes, and have high optical-to-near-infrared transmission. However, the effective coherence length (r0) on each of the fabricated screens is systematically too large or, equivalently, the fabricated aberrations are too weak. Despite this strong caveat, the screens appear to be quite useful: Long-exposure point-spread functions have realistic shapes, and power spectrum indices closely match those of the computer-generated wave fronts. Most significant, stacking screens with similar r0 values reduced r0 by the amount predicted by turbulence theory. The refractivity of MSI screens remains unmeasured. Finally, we present our design of an optical system that emulates the key characteristics of the Very Large Telescope, made to contain glass phase screens and to mimic an array of stars for multiconjugate adaptive optics system testing.