The prediction of sound transmission through buildings using statistical energy analysis

Measurements were carried out on a building to evaluate the uses of statistical energy analysis for determining sound transmission performance. Coupling loss factors were measured and compared with predicted values. It was found that, in general, good agreement was obtained. The coupling loss factors were also used to calculate the sound pressure level, or surface velocity, of each subsystem in the building for a number of different sources. Comparison with the measured results gave an average error of 4 dB. Some large errors were obtained but these were due mainly to the omission of airborne flanking paths from the SEA model or due to the breakdown of the theory for specific coupling loss factors.     

Numerically accurate computational techniques for optimal estimator analyses of multi-parameter models

Modelling unclosed terms in partial differential equations typically involves two steps: First, a set of known quantities needs to be specified as input parameters for a model, and second, a specific functional form needs to be defined to model the unclosed terms by the input parameters. Both steps involve a certain modelling error, with the former known as the irreducible error and the latter referred to as the functional error. Typically, only the total modelling error, which is the sum of functional and irreducible error, is assessed, but the concept of the optimal estimator enables the separate analysis of the total and the irreducible errors, yielding a systematic modelling error decomposition. In this work, attention is paid to the techniques themselves required for the practical computation of irreducible errors. Typically, histograms are used for optimal estimator analyses, but this technique is found to add a non-negligible spurious contribution to the irreducible error if models with multiple input parameters are assessed. Thus, the error decomposition of an optimal estimator analysis becomes inaccurate, and misleading conclusions concerning modelling errors may be drawn. In this work, numerically accurate techniques for optimal estimator analyses are identified and a suitable evaluation of irreducible errors is presented. Four different computational techniques are considered: a histogram technique, artificial neural networks, multivariate adaptive regression splines, and an additive model based on a kernel method. For multiple input parameter models, only artificial neural networks and multivariate adaptive regression splines are found to yield satisfactorily accurate results. Beyond a certain number of input parameters, the assessment of models in an optimal estimator analysis even becomes practically infeasible if histograms are used. The optimal estimator analysis in this paper is applied to modelling the filtered soot intermittency in large eddy simulations using a dataset of a direct numerical simulation of a non-premixed sooting turbulent flame.     

A numerical source of small-scale number-density fluctuations in Eulerian–Lagrangian simulations of multiphase flows

Eulerian–Lagrangian simulations of multiphase flow are known to suffer from two errors that can introduce small-scale fluctuations in the number-density of the dispersed phase. These errors can be reduced by increasing the number of particles in the simulation. Here, we present results to demonstrate that a third error exists that can also generate small-scale number-density fluctuations. In contrast to the two known errors, this error cannot be lowered by increasing the number of particles. Analysis shows that this error is caused by spatial variation at the subgrid scale in the interpolation error of the fluid velocity to the particle location. If the particle velocity divergence is zero, the particle concentration error remains at the subgrid scale. However, if particles preferentially accumulate either due to their inertia or due to divergence of the underlying fluid-velocity field, this error manifests as number-density fluctuations on the grid scale. The only mechanism of reducing these errors is through higher-order accurate interpolation. By studying two model problems, estimates for the errors are derived. These estimates are shown to be quite accurate for simulations of shock and expansion waves interacting with particles.     

Localization and delocalization errors in density functional theory and implications for band-gap prediction

The band-gap problem and other systematic failures of approximate exchange-correlation functionals are explained from an analysis of total energy for fractional charges. The deviation from the correct intrinsic linear behavior in finite systems leads to delocalization and localization errors in large and bulk systems. Functionals whose energy is convex for fractional charges such as the local density approximation display an incorrect apparent linearity in the bulk limit, due to the delocalization error. Concave functionals also have an incorrect apparent linearity in the bulk calculation, due to the localization error and imposed symmetry. This resolves an apparent paradox and identifies the physical nature of the error to be addressed to obtain accurate band gaps from density functional theory.     

Natural patterns of energy dispersal

Universal patterns such as power-law dependences, skewed distributions, tree-like structures, networks and spirals are associated with energy dispersal processes using the principle of least action. Also ubiquitous temporal courses such as sigmoid growth, bifurcations and chaos are ascribed to the decrease of free energy in the least time. Moreover, emergence of natural standards such as the common genetic code and chirality consensus of amino acids are understood to follow from the quest to maximize the dispersal of energy. Many mathematical functions that model natural patterns and processes are found as approximations of the evolutionary equation of motion that has been derived from statistical physics of open systems. The evolutionary processes can be described as flows of energy that run from high energy sources to low energy sinks in the least time. However, the equation of evolution cannot be solved in general because the flows of energy and their driving forces are inseparable. Since the energy of the system keeps changing, the paths of evolution cannot be integrated from a given initial state to a final state. Although evolutionary courses of these non-Hamiltonian systems with two or more alternative ways of dissipation cannot be predicted, the flows of energy will search and naturally select paths of least action, known as geodesics, to consume free energy in the least time. The scale-invariant natural patterns follow from this natural law that impinges on processes at all scales of space and time.     

Systematic error correction of a 3D laser scanning measurement device

Non-contact measurement techniques using laser scanning have the advantage of fast acquiring large numbers of points. However, compared to their contact-based counterparts, these techniques are known to be less accurate. The work presented in this paper aims at improving the accuracy of these techniques through an error correction procedure based on an experimental process that concerns mechanical parts. The influence of the three parameters, defining the relative position and the orientation between the sensor and the surface, is studied. The process used to build an experimental global model of error is presented and applied to a typical part composed of planes or skewed surface. The systematic errors have been reduced by half in comparison to the reference values, while the random errors have slightly increased. This phenomenon is due to the fact that the errors correction model does not take into account the local response of the laser sensor. A second model, taking into account the local defect, has been developed. Its application to an example of inspection of a mechanical part shows an improvement of the results of the correction.     

遥感数据误差对地表参数定量反演可靠性的影响——以太湖叶绿素a反演为例

地表参数的遥感反演误差的大小由遥感数据误差和反演模型误差共同构成,数据误差不是简单地“加减”到反演误差中,而是经过反演模型改造后融入到反演误差中。因此,在地表参数定量反演过程中,用回归系数最大或均方根误差最佳代价函数来描述地表参数与遥感反射光谱之间的关系将不太可靠。从理论上指出了最高回归系数或最小均方根误差评价方法失效的根源在于反演模型的形式,以2003年10月27日太湖实测数据为例进行了论证。研究表明,虽然TM2/TM3算法比TM2/TM1算法的回归系数高,但其对数据误差的放大效果是TM2/TM算法的2.28倍,这导致了反演结果的均方根误差比TM2/TM1算法大了7.938 5 μg·L-1;另外从定量反演结果来看,基于TM2/TM3算法和基于TM2/TM1算法的反演结果完全相反,与以往研究成果对比可知,基于TM2/TM1算法的反演结果更符合实际。因此,数据误差应该作为一个约束条件,加入到代价函数的求解过程中,才能增加反演结果的可靠性。     

Bayesian error estimation in density-functional theory

We present a practical scheme for performing error estimates for density-functional theory calculations. The approach, which is based on ideas from Bayesian statistics, involves creating an ensemble of exchange-correlation functionals by comparing with an experimental database of binding energies for molecules and solids. Fluctuations within the ensemble can then be used to estimate errors relative to experiment on calculated quantities such as binding energies, bond lengths, and vibrational frequencies. It is demonstrated that the error bars on energy differences may vary by orders of magnitude for different systems in good agreement with existing experience.     

基于多层介质膜光栅的谱合成系统光束特性分析

针对多层介质膜光栅在光束谱合成系统中的应用, 利用光线追迹方法, 建立了基于多层介质膜光栅的谱合成系统光传输模型. 多层介质膜光栅引入的相位调制包括浮雕表面上光程差与浮雕结构光程差两部分, 且受到光栅槽深、占空比和光束入射角等因素的影响. 利用衍射积分方法和光束非相干叠加原理, 计算模拟了基于多层介质膜光栅的谱合成系统的合成光束光强分布. 在此基础上, 利用强度二阶矩方法分析了合成光束的光束质量, 并讨论了多层介质膜光栅的槽深、占空比和制作误差等因素对合成光束特性的影响. 结果表明: 改变多层介质膜光栅的槽深和占空比以及中心光束入射角会影响合成光束能量, 但不会影响合成光束的光束质量, 合成光束的光束质量始终保持与单个子光束的光束质量相当; 多层介质膜光栅的制作误差对合成光束的光束质量和能量均存在明显影响.     

Two-line planar fluorescence for temporally resolved temperature imaging in a reacting supersonic flow over a body

An instantaneous temperature imaging technique for chemically reacting, supersonic flows over bodies is described and demonstrated in a H₂/O₂/Ar shock tube flow (M=1.3, 0.7 atm, 1760K freestream). Based on a planar fluorescence measurement, the approach uses a two-line rotational population ratio to infer temperature. The measured 2-d temperature profiles qualitatively match the expected flowfield structure around the blunt body, and the temperature increase across the bow shock in a single-shot measurement agrees within 5–10% of the prediction of a 1-d shock analysis. The significant systematic error sources for the technique are detailed, and the random error effects associated with shot-noise-limited fluorescence images are statistically analyzed to identify transitions which minimize the temperature errors for instantaneous and average measurements. Even for average temperature measurements, the analysis predicts errors which can be as large as 5–10% when noisy fluorescence images are used in conjunction with low temperature sensitivity. In general, temperature errors can be reduced by increasing sensitivity, i.e., the energy separation of the two rotational levels, until the fluorescence shot-noise rises to a value of 30–50% within the temperature range of interest.     

加工误差引入的薄型KDP晶体附加面形

针对惯性约束聚变（ICF）驱动装置中口径为400 mm400 mm薄型频率转换KDP晶体在45放置状态下产生的附加面形问题,采用有限元分析软件ANSYS,建立了以实测数据为基础的大口径薄型KDP晶体的应变模型和有加工误差的夹具模型,仿真分析了KDP晶体的加工误差和夹具的加工误差对KDP晶体附加面形的影响, 给出了KDP晶体附加面形变化的P-V值和RMS值。在此基础上,通过对KDP晶体的加工误差及夹具支撑表面不同类型和不同大小加工误差的分析和比较,得出:KDP晶体边缘的加工误差和夹具支撑表面的凹型加工误差是引起较大附加面形的原因之一,KDP晶体的加工误差也会导致其面形变化不均匀,而夹具支撑表面的凸型、波浪形加工误差和压条表面的随机加工误差对KDP晶体附加面形的影响相对较小,且支撑表面的随机加工误差引起的附加面形变化介于其他两者之间。     

About intrinsic errors of optical planarity measurements

We analyze the errors of optical 3D area sensors in measuring geometric parameters, taking planarity as our example. If the planarity of the surface is comparable to the repeat accuracy, the measured planarity is in general unduly poor and the object appears less planar. This error manifests itself to the observer as an apparently systematic offset. This error arises from the interplay of typical properties of optical sensors with standardized methods of interpretation. The standardized interpretation methods for planarity require the use of the maximum departures of the measured heights from the fitted (reference) plane. Optical area sensors can yield very large values for this maximum deviation, even when the standard deviation is small, because these sensors measure up to a million points at a time. The probability of a large maximum error is much lower when the measurement is done on a few points, as it usually is with mechanical sensors. As a consequence, the qualification of optical 3D area sensors calls for a correction with respect to mechanical sensors. In this article, we use methods of extreme-value statistics to determine the errors that occur. Once the error is known, the measured results can be corrected and incorporated into known and standardized methods of interpretation.     

光纤陀螺惯导系统航位推算误差补偿方法研究

 针对惯导系统定位误差随时间积累而增大的缺点,提出利用航位推算方法进行误差补偿。在航位推算中根据引起误差的主要因素推导出位置误差方程,以此方程为依据,建立相应的卡尔曼滤波器。将惯导系统速度与航位推算速度之差作为滤波器的输入,估计系统的姿态、速度、位置及里程计刻度系数误差值,并通过闭环反馈进行实时误差补偿修正。任选2条非闭合路径进行跑车实验,第一条路径定位误差补偿修正前是3.49‰,补偿修正后定位误差是2.3‰,第二条路径补偿修正前定位误差是2.4‰,补偿修正后定位误差是2‰。实验结果表明：采用航位推算误差补偿方法可以有效降低系统定位误差。     

序加实验理论模型误差修正的研究

针对序进应力加速实验理论模型中数学算法的误差,提出一种新的计算模型,新模型利用计算机编程辅助计算,显著地减小了模型误差.利用新、旧模型算法对理论数据进行计算,表明原模型算法存在13%以上的激活能计算误差以及150%以上的寿命计算误差（Q≤10　eV）,而新模型算法可以将激活能误差控制在1%以内,寿命计算误差控制在-41%以内. 关键词： 加速实验 序进应力 理论模型 误差修正     

Mutual alignment errors analysis based on wavelet due to antenna deformations in inter-satellite laser communications

Wavelet analysis is employed in the paper to model diversified optical antenna deformations in inter-satellite laser communications. Mutual alignment errors, which comprise pointing and tracking errors, caused by the deformations are investigated with the model. Theoretical and numerical analysis show that both errors increase with the dilation factor of the model. Tracking error increases monotonously with the shift factor of the model, while pointing error increases first, and then decreases. When the deformation can be well approximated to a constant, both errors fluctuate periodically with the coefficient of the model. Otherwise, there is no obvious regularity for both errors with the increase of the coefficient. A reference for the machining precision of optical antennas is presented, and a method to reduce the effect of deformations is recommended. It is hoped that the study can contribute to improve the performance of inter-satellite laser communication systems.     

运动轨迹对抛光误差的影响分析和轨迹优化研究

针对现有光学加工抛光头运动方式由于光栅形或螺旋形等对称扫描方式带来的运动轨迹间的迭代误差,提出随机轨迹抛光运动方式.随机轨迹方法通过随机轨迹算法随机生成镜面离散点的抛光顺序和抛光轨迹,采用随机轨迹驻留时间补偿方法控制镜面离散点的驻留时间,对各个点进行相应大小的材料去除.实验结果显示,随机轨迹方法产生的抛光运动轨迹表现为...     

Uncertainty analysis in matched-field geoacoustic inversions

Quantifying uncertainty for parameter estimates obtained from matched-field geoacoustic inversions using a Bayesian approach requires estimation of the uncertainties in the data due to ambient noise as well as modeling errors. In this study, the variance parameter of the Gaussian error model, hereafter called error variance, is assumed to describe the data uncertainty. In practice, this parameter is not known a priori, and choosing a particular value is often difficult. Hence, to account for the uncertainty in error variance, several methods are introduced for implementing both the full and empirical Bayesian approaches. A full Bayesian approach that permits uncertainty of the error variance to propagate through the parameter estimation processes is a natural way of incorporating the uncertainty of error variance. Due to the large number of unknown parameters in the full Bayesian uncertainty analysis, an alternative, the empirical Bayesian approach, is developed, in which the posterior distributions of model parameters are conditioned on a point estimate of the error variance. Comparisons between the full and empirical Bayesian inferences of model parameters are presented using both synthetic and experimental data.     

Analysis and modeling of radiometric error caused by imaging blur in optical remote sensing systems

Imaging blur changes the digital output values of imaging systems. It leads to radiometric errors when the system is used for measurement. In this paper, we focus on the radiometric error due to imaging blur in remote sensing imaging systems. First, in accordance with the radiometric response calibration of imaging systems, we provide a theoretical analysis on the evaluation standard of radiometric errors caused by imaging blur. Then, we build a radiometric error model for imaging blur based on the natural stochastic fractal characteristics of remote sensing images. Finally, we verify the model by simulations and physical defocus experiments. The simulation results show that the modeling estimation result approaches to the simulation computation. The maximum difference of relative MSE (Mean Squared Error) between simulation computation and modeling estimation can achieve 1.6%. The physical experimental results show that the maximum difference of relative MSE between experimental results and modeling estimation is only 1.29% under experimental conditions. Simulations and experiments demonstrate that the proposed model is correct, which can be used to estimate the radiometric error caused by imaging blur in remote sensing images. This research is of great importance for radiometric measurement system evaluation and application.     

Optimal network kinetics: A new significance to the principle of least time

The principle of least time is given a precise mathematical formulation in the new context of stochastic processes, where it is referred to as “optimal network kinetics”: In situations influenced by natural selection the efficient processes take place along optimal reaction coordinate paths, which in complex systems may form a network by bifurcations. The optimal paths in the configuration space of the system are defined by monimizing the time scale associated with an individual path in the set of all possible paths, subject to given boundary conditions. In particular it is discussed how optimal paths may be the consequence of detailed balance, which incorporates into the structure of the stochastic matrix of the system a local bias against excessive energy expenditure. Hence the optimal path depends on the configuration space (potential-) energy surface as well as on the temperature, for instance according to the law of Arrhenius at the crossing of a barrier along a reaction coordinate passing through the saddle-points. Exact formulations are given for disordered structures, including the case of variable range hopping conduction, where we obtain an exact derivation of the law of Mott. A variational formulation is given for processes corresponding to classical diffusion on a multidimensional energy surface. The corresponding differential equations defining the optimal path in this space have the form of newtonian equations of motion. However, the situation implies an interesting teleological aspect, which is unlike anything known from conventional dynamics. In order to be capable of crossing energy barriers the point tracing out the optimal path between given endpoints adjusts its mass so that both positive and negative values permit it to go along with, as well as against the locally acting force (the conventional gradient of the energy surface). At any point the appropriate mass, and hence the acceleration that is derived from the force at the current location, depends in a definite way on the entire path that is ultimately going to be completed.     

The prediction of airborne sound transmission between two rooms using first-order flanking paths

Airborne sound transmission between adjacent rooms can be predicted using the Standard EN 12354-1 (ISO 15712-1), which is equivalent to a first-order approximation of statistical energy analysis (SEA). This paper analyses airborne sound transmission between adjacent rooms in a masonry building, by comparing results obtained from EN 12354-1 to SEA predictions and measurements. It is shown that the restriction of the Standard to first-order flanking paths can lead to large errors in predictions when compared to measurements and SEA results taking into account all transmission paths. This is observed both for individual flanking paths and overall transmission between rooms, for which the Standard provides results similar to those obtained by the first-order approximation of SEA. The paper also looks at possible reasons why previous studies using the approach in EN 12354 have generally shown good agreement with measurements.