Optimization of a laser satellite communication system with an optical preamplifier

We derive a model that optimizes the performance of a laser satellite communication link with an optical preamplifier in the presence of random jitter in the transmitter-receiver line of sight. The system utilizes a transceiver containing a single telescope with a circulator. The telescope is used for both transmitting and receiving and thus reduces communication terminal dimensions and weight. The optimization model was derived under the assumption that the dominant noise source was amplifier spontaneous-emission noise. It is shown that, given the required bit-error rate (BER) and the rms random pointing jitter, an optimal transceiver gain exists that minimizes transmitted power. We investigate the effect of the amplifier spontaneous-emission noise on the optimal transmitted power and gain by performing an optimization procedure for various combinations of amplifier gain and noise figure. We demonstrate that the amplifier noise figure determines the optimal transmitted power needed to achieve the desired BER but does not affect the optimal transceiver telescope gain. Our numerical example shows that for a BER of 10(-9), doubling the amplifier noise figure results in an 80% increase in minimal transmitted power for a rms pointing jitter of 0.44 microrad.     

Digital simulation of two-dimensional random fields with arbitrary power spectra and non-Gaussian probability distribution functions

Methods for simulation of two-dimensional signals with arbitrary power spectral densities and signal amplitude probability density functions are disclosed. The method relies on initially transforming a white noise sample set of random Gaussian distributed numbers into a corresponding set with the desired spectral distribution, after which this colored Gaussian probability distribution is transformed via an inverse transform into the desired probability distribution. In most cases the method provides satisfactory results and can thus be considered an engineering approach. Several illustrative examples with relevance for optics are given.     

Performance of binary DS‐SSMA communications through Nakagami fading channel

Abstract

A binary asynchronous direct sequence spread spectrum multiple access system through Nakagami's m‐distributed channel is considered for non‐diversity receptions. Effects of fading and multiple access interferences on the average error probability are investigated. Approximation method to the average error probability is evaluated in two steps based on the moments of multiple access interferences and Nakagami distributions. Gauss quadrature rule is applied to evaluate the conditional probability conditioned on a fixed m‐distributed fading amplitude of the desired signal. Average error probability is then evaluated by the trapezoidal integration which integrates the conditional probability and the m‐distributed probability density function of the desired signal. This method provides a good approximation to the average error probability when the number of simultaneous users is large. Numerical results for the pseudorandom codes of code length 31 and Gold codes of code length 31 and 127 are presented.     

Robust consideration of importance sampling in digital communication system

Abstract

This paper proposes using a mixed biasing distribution in Importance Sampling for estimating the bit error rate (BER) via Monte Carlo simulation. The proposed mixed biasing distribution is more robust than the commonly used Gaussian tail distribution when the signal or the threshold setting is disturbed by a uniformly distributed random noise. In this paper the robustness is quantified by the mean squared error.     

遗传算法加权中值滤波器的优化设计

当测试数据中随机干扰满足高斯分布时,可以采用线性滤波器进行信号处理得到所要求的有用信号.而当随机干扰为非高斯分布时,则必须采用非线性的信号处理方法才能获得所要求的有用信号.这里讨论一类非线性滤波器——加权中值滤波器的最优设计问题.取损失函数为绝对误差的数学期望值,采用实数值编码多子种群的标准遗传算法来极小化损失函数.由于遗传算法:是用点群进行寻优,而不是用一个单点进行寻优,具有隐含并行算法的特点;群体在每一代的进化过程中执行同样的复制、交叉、变异操作,仅使用问题本身所对应的适应度函数,而不需要任何其它先决条件或辅助信息;遗传算法使用随机转换规则,而不是确定性规则进行运算.遗传算法作为一类全局最优算法,它所得到的加权中值滤波器也是全局最优的.数值计算结果表明,采用遗传算法可以得到更小的绝对误差平均值,且优于LMA算法.     

Dynamic Performance of Stacked Packaging Units

Stacked packaging units is the main form of distribution packaging of products. Its dynamic performance is not fully understood. This paper investigated the influence of the constraint, input vibration, location and contact nonlinearity on the dynamic performance of three layers stacked packaging units. The dynamic contact force between surfaces and acceleration response of products were obtained. In sine sweep vibrations, the constraint to stacked packaging units has an obvious influence on the dynamic characteristics. The acceleration response of product is associated with the vibration mode. The force amplification factor is in general between 1.5 and 2, but it can close to 3 on top layer in the case of no fixed. In random vibrations, non‐Gaussian data of dynamic contact force appear when Gaussian data of input vibration pass through the stacked packaging units, resulting a Weibull distribution of force level‐crossing. The force level‐crossing diagram becomes more abrupt with the decreasing of input vibration level, smoother from the top contact surface to middle and bottom ones, and moves right and becomes smoother with the constraint strengthen. In the case of lower input level, Gaussian distribution of force level‐crossing appears. The force power spectral density (PSD) between bottom box and table is much larger than that between boxes, which is significantly influenced by the first resonance frequency. However, the acceleration PSD of product is significantly influenced by both the first and second resonance frequencies, and controlled by the vibration mode. It depends much on the value of input acceleration PSD around the resonance frequencies.     

Construction of probability distributions in high dimension using the maximum entropy principle: Applications to stochastic processes,random fields and random matrices

The construction of probabilistic models in computational mechanics requires the effective construction of probability distributions of random variables in high dimension. This paper deals with the effective construction of the probability distribution in high dimension of a vector‐valued random variable using the maximum entropy principle. The integrals in high dimension are then calculated in constructing the stationary solution of an Itô stochastic differential equation associated with its invariant measure. A random generator of independent realizations is explicitly constructed in this paper. Three fundamental applications are presented. The first one is a new formulation of the stochastic inverse problem related to the construction of the probability distribution in high dimension of an unknown non‐stationary random time series (random accelerograms) for which the velocity response spectrum is given. The second one is also a new formulation related to the construction of the probability distribution of positive‐definite band random matrices. Finally, we present an extension of the theory when the support of the probability distribution is not all the space but is any part of the space. The third application is then a new formulation related to the construction of the probability distribution of the Karhunen–Loeve expansion of non‐Gaussian positive‐valued random fields. Copyright © 2008 John Wiley & Sons, Ltd.     

A stochastic simulation method for uncertainty quantification in the linearized inverse conductivity problem

This paper considers the inverse problem in electrical impedance tomography with non‐informative prior information on the required conductivity function. The problem is approached with a Newton‐type iterative algorithm where the solution of the linearized approximation is estimated using Bayesian inference. The novelty of this work focuses on maximum a posteriori estimation assuming a model that incorporates the linearization error as a random variable. From an analytical expression of this term, we employ Monte Carlo simulation in order to characterize its probability distribution function. This simulation entails sampling an improper prior distribution for which we propose a stable scheme on the basis of QR decomposition. The simulation statistics show that the error on the linearized model is not Gaussian, however, to maintain computational tractability, we derive the posterior probability density function of the solution by imposing a Gaussian kernel approximation to the error density. Numerical results obtained through this approach indicate the superiority of the new model and its respective maximum a posteriori estimator against the conventional one that neglects the impact of the linearization error. Copyright © 2011 John Wiley & Sons, Ltd.     

Statistical modelling of predicted non‐stationary vehicle vibrations

This paper describes a method to predict the vertical vibrations of road vehicles from measured pavement profiles. It discusses the limitations of current methods used for analysing and simulating vehicle vibrations and shows that more accurate characterization and simulation of the transport environment must take into account the non‐stationary nature of road vehicle vibrations. Vertical vibrations for typical transport vehicles under various operating conditions and pavement profiles are predicted using a computer model of the vehicle characteristics and analysed to produce the spectral and statistical characteristics. The paper also presents an improved method to compute the vibration intensity by using a dynamic segmentation data reduction technique. The effectiveness of the procedure to characterize the non‐stationarity of random vehicle vibrations is demonstrated. Finally, the paper deals with the statistical distribution of the vibration intensity and demonstrates how it can be adapted to a technique for the simulation the non‐stationary nature of random vehicle vibrations. Copyright © 2002 John Wiley & Sons, Ltd.     

Using the Weibull distribution to characterise road transport vibration levels

This paper reviews the various ways that have been proposed to characterise road transport vehicle vibrations and recommends a new approach to characterise the vibrations levels during a transport journey. Some 47 road vehicle vibration records, obtained from a broad range of conditions, were analysed, and results show that the root-mean-square (rms) distribution of the vibrations can be accurately modelled with a reduced version of the three-parameter Weibull distribution (shape parameter set to 2). This statistical approach to characterising road vehicle vibrations takes into account the random fluctuations in rms levels that occur naturally during a road journey and can be used to classify the severity of RVV. This offers significant improvement on the simplistic mean rms value that has, so far, been the sole parameter to describe vibration levels during transport. The Weibull location parameter represents the low threshold of the rms level in the record (except when xo is less than zero, in which case the low rms threshold is zero), whereas the Weibull range parameter is proportional to the range of rms level. Results also reveal a strong relationship between the rms mean and the sum of the location and scale parameters. In addition, this enables generation of rms distributions from the mean power density spectrum (PDS) alone. The modified (fixed-shape) Weibull distribution can be used to faithfully describe the entire statistical distribution of the rms level of a journey or transport mode with just two parameters. This new approach can be used in a practical way for quantifying and comparing transport vibration rms levels for design and testing purposes.     

Statistical reconstruction and Karhunen–Loève expansion for multiphase random media

Termed as random media, rocks, composites, alloys and many other heterogeneous materials consist of multiple material phases that are randomly distributed through the medium. This paper presents a robust and efficient algorithm for reconstructing random media, which can then be fed into stochastic finite element solvers for statistical response analysis. The new method is based on nonlinear transformation of Gaussian random fields, and the reconstructed media can meet the discrete‐valued marginal probability distribution function and the two‐point correlation function of the reference medium. The new method, which avoids iterative root‐finding computation, is highly efficient and particularly suitable for reconstructing large‐size random media or a large number of samples. Also, benefiting from the high efficiency of the proposed reconstruction scheme, a Karhunen–Loève (KL) representation of the target random medium can be efficiently estimated by projecting the reconstructed samples onto the KL basis. The resulting uncorrelated KL coefficients can be further expressed as functions of independent Gaussian random variables to obtain an approximate Gaussian representation, which is often required in stochastic finite element analysis. Copyright © 2015 John Wiley & Sons, Ltd.     

Practical choices in the FRF measurement in presence of nonlineardistortions

The frequency response function (FRF) of the best linear approximation to a nonlinear system is usually measured by averaging system responses to a normally distributed, filtered, and clipped random excitation (Gaussian noise). This signal is compared to the multisine signal with random phases. It is shown that a random phase multisine signal defined over an even-odd frequency grid is superior to the Gaussian signal in terms of the variance and the bias of the measured FRF of the approximated nonlinear system     

MIMO线性系统输入输出信号统计特征的双谱评定方法

基于高阶统计量具备处理随机信号的特性,提出了一种利用三阶谱(双谱)评定MIMO线性系统时域输入输出信号统计特征的新方法。通过建立线性系统双谱数学模型,根据系统响应、所测得的频响函数以及离散信号的双谱数值估计算法,经逆运算获得系统的双谱驱动信号,随后利用高阶谱对高斯随机信号的盲性判定其输入信号的高斯性。将上述方法与采用传统相位随机化法(对功率谱添加随机相位)所获得的驱动信号分别应用于一悬臂梁模拟控制系统中,通过对输入信号的分析及控制结果的比较,发现基于双谱所生成的时域随机驱动信号呈现出较强的非高斯性且收敛速度更快。对于输出信号统计特征的评定,提出从输入信号与系统频带接近的程度入手,再次利用高阶统计量对高斯随机信号的盲性进行定性判定,对于无法判别满足何种非高斯统计分布特征的,不管是对于输入信号还是输出信号,一律采用绘制信号的概率分布特征曲线进行定量评定。     

A non‐intrusive model reduction approach for polynomial chaos expansion using proper orthogonal decomposition

In this paper, a non‐intrusive stochastic model reduction scheme is developed for polynomial chaos representation using proper orthogonal decomposition. The main idea is to extract the optimal orthogonal basis via inexpensive calculations on a coarse mesh and then use them for the fine‐scale analysis. To validate the developed reduced‐order model, the method is implemented to: (1) the stochastic steady‐state heat diffusion in a square slab; (2) the incompressible, two‐dimensional laminar boundary‐layer over a flat plate with uncertainties in free‐stream velocity and physical properties; and (3) the highly nonlinear Ackley function with uncertain coefficients. For the heat diffusion problem, the thermal conductivity of the slab is assumed to be a stochastic field with known exponential covariance function and approximated via the Karhunen–Loève expansion. In all three test cases, the input random parameters are assumed to be uniformly distributed, and a polynomial chaos expansion is found using the regression method. The Sobol's quasi‐random sequence is used to generate the sample points. The numerical results of the three test cases show that the non‐intrusive model reduction scheme is able to produce satisfactory results for the statistical quantities of interest. It is found that the developed non‐intrusive model reduction scheme is computationally more efficient than the classical polynomial chaos expansion for uncertainty quantification of stochastic problems. The performance of the developed scheme becomes more apparent for the problems with larger stochastic dimensions and those requiring higher polynomial order for the stochastic discretization. Copyright © 2015 John Wiley & Sons, Ltd.     

Quantifying the Non‐stationarity of Vehicle Vibrations with the Run Test

This paper investigates the applicability of the run test as a tool to quantify the statistical non‐stationarity of road vehicle vibrations. The run test was applied to the moving root‐mean‐square (RMS) time history of a number of vibration records measured from a variety of vehicle types, routes and vehicle speeds. The paper discusses the limitations associated with calculating the moving RMS of random signals especially with respect to the window width. When applied to the set of vibration records (with segments of inactivity removed), the run test indicates that every record is non‐stationary. A run ratio parameter was introduced to quantify the level of non‐stationarity, which shows that the result is sometimes dependent on the RMS window width. Further analysis correlating the run test results with the statistical distribution or the RMS indicates that the run ratio parameter has some merit in quantifying the level of non‐stationarity in road vehicle vibrations. Copyright © 2013 John Wiley & Sons, Ltd.     

On the application of the stochastic approach in predicting fatigue reliability using Miner's damage rule

The present paper investigates the application of the stochastic approach when the commonly adopted Miner's linear damage rule is implemented, both in its traditional and modified forms to include the presence of a random stress threshold (random fatigue limit), below which the rate of damage accumulation is reduced. Main steps are provided to obtain the simulated distribution of the accumulated damage under variable amplitude loading. When the stochastic approach is applied in the presence of a random fatigue limit, an additional correlation structure, which takes into account the fatigue limit value, must be introduced in the analysis. If the number of cycles to failure under constant amplitude loading is Weibull (Log‐Normal) distributed, then the corresponding accumulated damage is Fréchet (Log‐Normal) distributed. The effects of the correlation structure on reliability prediction under variable amplitude loading are also investigated. To this aim, several experimental datasets are taken from the literature, covering various metallic materials and variable amplitude block sequences. The results show that the choice of the damage accumulation model is a key factor to value the improvement in the accuracy of reliability predictions introduced by the stochastic approach. Comparison of the predicted number of cycles to failure with experimental data shows that larger errors are non‐conservative, regardless of the adopted correlation structure. When the analysis is limited to reliability levels above 80%, for these large non‐conservative errors, it is the quantile approach to be closer to actual experimental data, thus limiting the overestimation of component's life. For the experimental datasets considered in the paper, adoption of a stochastic approach would improve the accuracy of Miner's predictions in 10% of cases.     

Wave-front design algorithm for shaping a quasi-far-field pattern

To design a fully continuous wave-front distribution suitable for focused beam shaping by a deformable mirror, we modify the phase-retrieval algorithm by employing a uniformly distributed phase as a starting phase screen and spatial filtering for the near-field phase retrieved during the iteration process. A special phase unwrapping algorithm is not required to obtain a continuous phase distribution from the retrieved phase since the boundary of the 2pi-phase-jumped region in the designed phase distribution is perfectly closed. From the computational result producing a uniform square beam transformation from a circular defocused beam, this algorithm has provided a fully continuous wave-front distribution with a lower spatial frequency for a deformable mirror. The transformed square beam has a normalized intensity nonuniformity of varsigma(rms) = 0.14 with respect to a desired flat-topped square beam pattern. This beam-shaping method also provides a high energy-concentration rate of more than 98%.     

On the Use of Machine Learning to Detect Shocks in Road Vehicle Vibration Signals

The characterization of transportation hazards is paramount for protective packaging validation. It is used to estimate and simulate the loads and stresses occurring during transport that are essential to optimize packaging and ensure that products will resist the transportation environment with the minimum amount of protective material. Characterizing road transportation vibrations is rather complex because of the nature of the dynamic motion produced by vehicles. For instance, different levels of vibration are induced to freight depending on the vehicle speed and the road surface; which often results in non‐stationary random vibration. Road aberrations (such as cracks, potholes and speed bumps) also produce transient vibrations (shocks) that can damage products. Because shocks and random vibrations cannot be analysed with the same statistical tools, the shocks have to be separated from the underlying vibrations. Both of these dynamic loads have to be characterized separately because they have different damaging effects. This task is challenging because both types of vibration are recorded on a vehicle within the same vibration signal. This paper proposes to use machine learning to identify shocks present in acceleration signals measured on road vehicles. In this paper, a machine learning algorithm is trained to identify shocks buried within road vehicle vibration signals. These signals are artificially generated using non‐stationary random vibration and shock impulses that reproduce typical vehicle dynamic behaviour. The results show that the machine learning algorithm is considerably more accurate and reliable in identifying shocks than the more common approaches based on the crest factor. Copyright © 2016 John Wiley & Sons, Ltd.     

Linear random vibration by stochastic reduced‐order models

A practical method is developed for calculating statistics of the states of linear dynamic systems with deterministic properties subjected to non‐Gaussian noise and systems with uncertain properties subjected to Gaussian and non‐Gaussian noise. These classes of problems are relevant as most systems have uncertain properties, physical noise is rarely Gaussian, and the classical theory of linear random vibration applies to deterministic systems and can only deliver the first two moments of a system state if the noise is non‐Gaussian. The method (1) is based on approximate representations of all or some of the random elements in the definition of linear random vibration problems by stochastic reduced‐order models (SROMs), that is, simple random elements having a finite number of outcomes of unequal probabilities, (2) can be used to calculate statistics of a system state beyond its first two moments, and (3) establishes bounds on the discrepancy between exact and SROM‐based solutions of linear random vibration problems. The implementation of the method has required to integrate existing and new numerical algorithms. Examples are presented to illustrate the application of the proposed method and assess its accuracy. Copyright © 2009 John Wiley & Sons, Ltd.