Iterative simulated quenching for designing irregular-spot-array generators

We propose a novel, to our knowledge, algorithm of iterative simulated quenching with temperature rescaling for designing diffractive optical elements, based on an analogy between simulated annealing and statistical thermodynamics. The temperature is iteratively rescaled at the end of each quenching process according to ensemble statistics to bring the system back from a frozen imperfect state with a local minimum of energy to a dynamic state in a Boltzmann heat bath in thermal equilibrium at the rescaled temperature. The new algorithm achieves much lower cost function and reconstruction error and higher diffraction efficiency than conventional simulated annealing with a fast exponential cooling schedule and is easy to program. The algorithm is used to design binary-phase generators of large irregular spot arrays. The diffractive phase elements have trapezoidal apertures of varying heights, which fit ideal arbitrary-shaped apertures better than do trapezoidal apertures of fixed heights.     

Frontiers in Statistical Quality Control 3

Computer model calibration is the process of determining input parameter settings to a computational model that are consistent with physical observations. This is often quite challenging due to the computational demands of running the model. In this article, we use the ensemble Kalman filter (EnKF) for computer model calibration. The EnKF has proven effective in quantifying uncertainty in data assimilation problems such as weather forecasting and ocean modeling. We find that the EnKF can be directly adapted to Bayesian computer model calibration. It is motivated by the mean and covariance relationship between the model inputs and outputs, producing an approximate posterior ensemble of the calibration parameters. While this approach may not fully capture effects due to nonlinearities in the computer model response, its computational efficiency makes it a viable choice for exploratory analyses, design problems, or problems with large numbers of model runs, inputs, and outputs.     

未知输入干扰下异构多传感器分布式两级信息滤波与偏差联合估计

针对目标跟踪过程中受未知输入影响的多传感器网络,提出一种局部单传感器抗干扰信息滤波算法并根据此算法实现分布式一致性多传感器融合滤波估计实现目标的精确跟踪。首先,建立包含未知输入的系统模型;其次,消除未知输入影响并设计局部单传感器两级信息滤波算法实现状态和广义偏差的同时估计;最后,根据提出的单传感器两级信息滤波算法进行分布式加权数据融合。仿真结果表明,该方法及其融合算法的系统偏差、状态估计误差和均方根误差均明显降低,目标跟踪精度有所提高,并且具有较低的运算量和较高的一致性。     

多相关子系统输入中源识别的分析研究

建立了子系统输入单输出系统模型,分析了双子系统输入单输出系统中各级输入之间的相关关系,给出了集合平均的输入关系式。在此基础上推导了多相关子系统输入各级输入之间的相关关系和集合平均输入模型。针对多相关子系统输入单输出系统中输入的源识别问题,分析了子系统各级输入各种相关情况下输入相关矩阵的数值变化以及对输出的影响,通过相干分析得到了判断子系统各级输入对输出贡献量的方法。最后给出了某汽车前后轴垂直平面内振动试验数据的处理结果,验证了理论分析的实用性。理论分析及试验对同类工程问题具有参考价值     

Relative contributions of aleatory and epistemic uncertainty sources in time series prediction

This paper develops a novel computational framework to compute the Sobol indices that quantify the relative contributions of various uncertainty sources towards the system response prediction uncertainty. In the presence of both aleatory and epistemic uncertainty, two challenges are addressed in this paper for the model-based computation of the Sobol indices: due to data uncertainty, input distributions are not precisely known; and due to model uncertainty, the model output is uncertain even for a fixed realization of the input. An auxiliary variable method based on the probability integral transform is introduced to distinguish and represent each uncertainty source explicitly, whether aleatory or epistemic. The auxiliary variables facilitate building a deterministic relationship between the uncertainty sources and the output, which is needed in the Sobol indices computation. The proposed framework is developed for two types of model inputs: random variable input and time series input. A Bayesian autoregressive moving average (ARMA) approach is chosen to model the time series input due to its capability to represent both natural variability and epistemic uncertainty due to limited data. A novel controlled-seed computational technique based on pseudo-random number generation is proposed to efficiently represent the natural variability in the time series input. This controlled-seed method significantly accelerates the Sobol indices computation under time series input, and makes it computationally affordable.     

Error estimation in a stochastic finite element method in electrokinetics

Input data to a numerical model are not necessarily well known. Uncertainties may exist both in material properties and in the geometry of the device. They can be due, for instance, to ageing or imperfections in the manufacturing process. Input data can be modelled as random variables leading to a stochastic model. In electromagnetism, this leads to solution of a stochastic partial differential equation system. The solution can be approximated by a linear combination of basis functions rising from the tensorial product of the basis functions used to discretize the space (nodal shape function for example) and basis functions used to discretize the random dimension (a polynomial chaos expansion for example). Some methods (SSFEM, collocation) have been proposed in the literature to calculate such approximation. The issue is then how to compare the different approaches in an objective way. One solution is to use an appropriate a posteriori numerical error estimator. In this paper, we present an error estimator based on the constitutive relation error in electrokinetics, which allows the calculation of the distance between an average solution and the unknown exact solution. The method of calculation of the error is detailed in this paper from two solutions that satisfy the two equilibrium equations. In an example, we compare two different approximations (Legendre and Hermite polynomial chaos expansions) for the random dimension using the proposed error estimator. In addition, we show how to choose the appropriate order for the polynomial chaos expansion for the proposed error estimator. Copyright © 2009 John Wiley & Sons, Ltd.     

列车垂向振动的半主动简谐隔振研究

依据拉格郎日方程,建立六自由度列车半主动隔振系统的垂向振动模型;应用MATLAB/SIMULINK仿真模块构造列车半主动隔振系统仿真模型,对列车进行时域分析。在轨道具有简谐输入的情况下对列车的隔振性能（如隔振位移、隔振传递率等）进行了计算分析,讨论了弹簧刚度、阻尼、车速、激励的波长等对隔振性能的影响。通过研究可得列车系统采用半主动开关阻尼器,确实能够改善系统的隔振性能。     

A comparison of transfer function estimators

The response of a linear time-invariant process on a stochastic input signal is characterized by the transfer function. Unknown past inputs and future output are sources of inaccuracy in relating a finite segment of an output signal via an estimated transfer function to the corresponding input segment. These end effects are usually characterized with error bounds on the Fourier transform of the output signal, but the error in an estimated transfer function can be quantified more precisely in terms of bias and variance. The accuracy of three transfer function estimators is compared, showing an infinite variance for the Experimental Transfer Function Estimate (ETFE) and a better efficiency for the estimators which are based on the cross spectrum. The variance due to additive noise depends on whether the input is a stochastic or a deterministic signal     

Phase-plane-derived distortion modeling of a fast and accurate digitizing sampler

Continued efforts to model the distortion behavior of custom-designed digitizing samplers for accurate measurement of dynamic signals are reported. This work is part of ongoing efforts at the National Institute of Standards and Technology (NIST) to advance the state of the art in waveform sampling metrology. In this paper, an analytic error model for a sampler having a -3-dB 6-GHz bandwidth is described. The model is derived from examination of the sampler's error behavior in the phase plane. The model takes as inputs the per-sample estimates of signal amplitude, first derivative, and second derivative, where the derivatives are with respect to time. The model's analytic form consists of polynomials in these terms, which are chosen from consideration of the voltage dependence of the digitizer input capacitance and the previously studied error behavior in a predecessor digitizer. At 1 GHz, an improvement in total harmonic distortion from -32 to -46 dB is obtained when model-generated sample corrections are applied to the waveform. The effect of timebase distortion in the sampling system is also accounted for and corrected. The inclusion of second-derivative dependence in the model is shown to improve the model's fit to the measured data by providing fine temporal adjustment of the fitted waveform.     

Nonlinear Systems Identification via an Input-Output Model Based on a Feedforward Neural Network

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Experimental analysis and modeling of hydronic radiant ceiling panels using transient-state analysis

The model developed in this investigation considers the hydronic panels as a transient-state heat exchanger connected to a detailed lumped transient model of the building. The behavior of the hydronic ceiling system and the interactions with its environment has been experimentally and numerically evaluated. This article presents the results of a study performed to develop a transient model of hydronic ceiling panels in heating or cooling modes and its environment (window, building structure, internal thermal loads and ventilation).Only the dry regime is considered in this case. Using as inputs the hydronic ceiling and room dimensions, material properties and the transient measurements of the air temperature at the adjacent zones, climatic conditions, supply air and water temperatures and mass flow rates, the model permits to estimate the water exhaust temperature, ceiling average surface temperature, resultant and dry air room temperatures, hydronic ceiling power and internal surface temperatures of the room in order to compare with measurements taken during the commissioning process. Two transient tests in heating and cooling modes are used to the experimental validation.     

Simulation of local material properties based on moving-window GMC

When analyzing the behavior of composite materials under various loading conditions, the assumption is generally made that the behavior due to randomness in the material can be represented by a homogenized, or effective, set of material properties. This assumption may be valid when considering displacement, average strain, or even average stress of structures much larger than the inclusion size. The approach is less valid, however, when considering either behavior of structures of size at the scale of the inclusions or local stress of structures in general. In this paper, Monte Carlo simulation is used to assess the effects of microstructural randomness on the local stress response of composite materials. In order to achieve these stochastic simulations, the mean, variance and spectral density functions describing the randomly varying elastic properties are required as input. These are obtained here by using a technique known as moving-window generalized method of cells (moving-window GMC). This method characterizes a digitized composite material microstructure by developing fields of local effective material properties. Once these fields are generated, it is straightforward to obtain estimates of the associated probabilistic parameters required for simulation. Based on the simulated property fields, a series of local stress fields, associated with the random material sample under uniaxial tension, is calculated using finite element analysis. An estimation of the variability in the local stress response for the given random composite is obtained from consideration of these simulations.     

Efficient spectral response of locally uncertain linear systems

It is difficult to model any real dynamical system with fully deterministic characteristics and yet, capture its behavior reasonably. Randomness arises from many sources, such as uncertain material properties, assumptions involved in structural modeling, and the stochastic nature of input forces. Thus, the random vibration analysis of systems with uncertain parameters is a crucial component of structural design and optimization procedures. In this paper, a new method is presented for fast spectral analysis of locally uncertain systems subjected to random inputs based on the response of one such system (called the nominal system). Unlike other methods, such as modal expansion methods, the proposed method is applicable to general uncertainties in the damping and stiffness matrices with the sole restriction that the system remains stable with probability one. Moreover, the proposed method yields exact responses for the perturbed systems and its accuracy is not affected by the size or magnitude of the uncertainties. However, the degree of locality of the uncertainty dictates the observed gains in computational efficiency when using the proposed method. When the uncertainty is extremely localized, one can expect gains in computational efficiency of two to three orders of magnitude while only modest gains of 2–3 times are observed when half the model is uncertain. Two numerical examples are presented to illustrate the accuracy and gains in computational efficiency of the proposed method.     

Random vibration analysis for train–track interaction from the aspect of uncertainty quantification

This work is devoted to constructing a stochastic analysis model for train–track​ interaction. The fundamentals of the modelling framework in the establishment of the dynamic model, simulation of system uncertainties and randomness propagation process have been properly illustrated and unified in detail. For modelling train–track interaction, a matrix representation method is developed to depict the displacement compatibility and force equilibrium between the train and tracks. This dynamic model possesses advantages in computational stability and accuracy. Using uncertainty quantification approaches, the randomness of system geometries and longitudinal inhomogeneity of system properties can be simulated properly. Finally, the probabilistic transmission between the system inputs and response outputs are investigated from physical concepts, and a family of probability density evolution methods is introduced. Following the fundamental framework of train–track stochastic analysis, numerical examples are presented in detail to show the efficiency and accurateness of the proposed model. Moreover, the applications and advancements of this model in reliability assessment, response and frequency analysis, derailment, etc., are illustrated.     

高速铁路客站大跨站厅结构竖向多点地震响应研究

"房桥合一"是我国高速铁路客站建造中出现的一种新型结构形式,其兼具房屋和桥梁结构特征,轨道层列车线路的通行要求决定了上部高架站厅层具有较大跨度,而站厅结构竖向抗震性能往往是确保其地震安全的重要部分。鉴于此,首先阐述了SAP2000软件中位移模型的基本计算原理,并指出其一重要误差,继而参考天津西站建立了典型大跨站厅结构模型,对比研究了竖向多点一致、考虑行波效应竖向多点非一致地震激励下典型站厅结构动力响应特征。研究表明:依据位移模型直接计算结果来获取不参与动力平衡方程的从属结构响应分量时可能存在明显误差;竖向多点非一致输入特征对高架站厅层的地震响应有着显著影响,在抗震设计和性能评估中均不可忽视此因素,同时给出了抗震设计建议。     

An approach for the Pasternak elastic foundation parameters estimation of beams using simulated frequencies

As a first attempt, a mix of differential quadrature (DQ) and simplex (S) method for the Pasternak elastic foundation parameters estimation of beams using simulated frequencies is presented. The method is applied for the parameters estimation of functionally graded (FG) beams. The first-order shear deformation theory is employed to derive governing equations of FG beam on the Pasternak elastic foundation. The equations are discretized by utilizing the DQ method and frequencies of the beam are calculated. Then, the simulated frequencies are obtained by applying random error to the calculated frequencies. The simulated frequencies are used as input data for estimating parameters of the problem. An objective function as a root-mean-square error between the calculated and simulated frequencies is defined. The DQ method and simplex technique as a classical optimization technique are coupled to minimize the function via finding the best foundation parameters, iteratively. Some examples are solved to show applicability, robustness and accuracy of the mixed method for elastic foundation parameters estimation of the beam. Also, it has been found that using only the first simulated frequency of the beam cannot give correct parameters of the foundation.     

起落架载荷标定模型的集成学习方法

为解决飞机起落架载荷标定实验使用线性回归建立标定方程结果不理想的问题,考虑到实验中起落架压缩行程和应变片布片位置等因素对标定载荷的非线性影响,运用特征融合、集成学习理论,通过使用AdaBoost和XGBoost非线性回归方法,构建起落架载荷标定模型。首先,通过起落架载荷标定实验获取实验数据,使用主成分分析方法建立输入特征矩阵;其次,构建起落架载荷标定模型,将起落架三向加载载荷分别作为标签向量,训练集和测试集根据随机取样原则划分,使用AdaBoost和XGBoost两种方法训练标定模型;最后,在测试集中对载荷进行拟合预测,并使用均方根误差、平均绝对误差、决定系数、耗时4个评价指标对模型进行评估。实验结果显示,与广泛使用的最小二乘法相比,XGBoost方法建立的标定模型能够更好地拟合加载载荷,在不考虑时效性的场景下XGBoost算法更具优势。研究结果对提高飞机起落架载荷实测准确性以及飞机结构健康监测的进一步研究具有重要价值。     

Frequency filtering in disordered granular chains

The study of disorder-induced frequency filtering is presented for one-dimensional systems composed of random, pre-stressed masses interacting through both linear and nonlinear (Hertzian) repulsive forces. An ensemble of such systems is driven at a specified frequency, and the spectral content of the propagated disturbance is examined as a function of distance from the source. It is shown that the transmitted signal contains only low-frequency components, and the attenuation is dependent on the magnitude of disorder, the input frequency, and the contact model. It is found that increased disorder leads to a narrower bandwidth of transmitted frequencies at a given distance from the source and that lower input frequencies exhibit less sensitivity to the arrangement of the masses. Comparison of the nonlinear and linear contact models reveals qualitatively similar filtering behavior; however, it is observed that the nonlinear chain produces transmission spectrums with a greater density at the lowest frequencies. In addition, it is shown that random masses sampled from normal, uniform, and binary distributions produce quantitatively indistinguishable filtering behavior, suggesting that knowledge of only the distribution’s first two moments is sufficient to characterize the bulk signal transmission behavior. Finally, we examine the wave number evolution of random chains constrained to move between fixed end-particles and present a transfer matrix theory in wave number space, and an argument for the observed filtering based on the spatial localization of the higher-frequency normal modes.     

扩展特征系统实现算法的模态参数识别特性研究

结构动力响应作为模态参数识别的输入数据,对识别结果存在一定的影响。扩展特征系统实现算法(EERA)是一种多输入输出的结构模态参数识别的时域方法,相比于特征系统实现算法(ERA)应用范围可以扩展到任何随机响应,具有识别精度高、稳定性好等特点。该文主要对EERA算法,在分别采用加速度、速度和位移动力响应作为输入时,对两个自由度弹簧阻尼质量系统和实验室环境下6层框架结构识别的结果进行了比较分析,得出EERA对任何动力响应均适用,并且建议采用加速度动力响应信号识别高阶模态。     

Temperature correction to chemoresistive sensors in an e-NOSE-ANN system

The influence of the temperature coefficient of resistance in the chemoresistive response of inherently conductive polymer (ICP) sensors in the performance of an artificial neural network (ANN) e-natural olfactory sensor emulator (e-NOSE) system is evaluated. Temperature was found to strongly influence the response of the chemoresistors, even over modest ranges (ca. 2/spl deg/C). An e-NOSE array of eight ICP sensor elements, a relative humidity (RH/spl plusmn/0.1%) sensor, and a resistance temperature device (RTD/spl plusmn/0.1/spl deg/C) was tested at five different RH levels while the temperature was allowed to vary with the ambient. A temperature correction algorithm based on the temperature coefficient of resistance /spl beta/ for each material was independently and empirically determined then applied to the raw sensor data prior to input to the ANN. Conversely, uncorrected data was also passed to the ANN. The performance of the ANN was evaluated by determining the error found between the actual humidity versus the calculated humidity. The error obtained using raw input sensor data was found to be 10.5% and using temperature corrected data, 9.3%. This negligible difference demonstrates that the ANN was capable of adequately addressing the temperature dependence of the chemoresistive sensors once temperature was inclusively passed to the ANN.