In this paper an efficient model based diagnostic process is described for
systems whose components possess a causal relation between their inputs and
their outputs. In this diagnostic process, firstly, a set of focuses on likely
broken components is determined. Secondly, for each focus the most informative
probing point within the focus can be determined. Both these steps of the
diagnostic process have a worst case time complexity of ${\cal O}(n^2)$ where
$n$ is the number of components. If the connectivity of the components is low,
however, the diagnostic process shows a linear time complexity. It is also
shown how the diagnostic process described can be applied in dynamic systems
and systems containing loops. When diagnosing dynamic systems it is possible to
choose between detecting intermitting faults or to improve the diagnostic
precision by assuming non-intermittency.

本文介绍了一种高效的模型诊断过程，针对具有输入输出因果关系的系统。在此诊断过程中，首先确定一组可能破损的组件的焦点；其次，在焦点内确定最具信息的探测点。该诊断过程在组件的连通性低时表现出线性时间复杂度，并可应用于动态系统和包含循环的系统中，可选择检测间歇性故障或通过假定非间歇性来提高诊断精度。

高效的基于模型的诊断

Efficient Model Based Diagnosis

Scattering moments provide nonparametric models of random processes with
stationary increments. They are expected values of random variables computed
with a nonexpansive operator, obtained by iteratively applying wavelet
transforms and modulus nonlinearities, which preserves the variance. First- and
second-order scattering moments are shown to characterize intermittency and
self-similarity properties of multiscale processes. Scattering moments of
Poisson processes, fractional Brownian motions, L\'{e}vy processes and
multifractal random walks are shown to have characteristic decay. The
Generalized Method of Simulated Moments is applied to scattering moments to
estimate data generating models. Numerical applications are shown on financial
time-series and on energy dissipation of turbulent flows.

本文探讨了散射矩提供了随机过程的非参数模型，散射矩通过应用小波变换和非线性模量来计算随机变量的期望值，能够揭示多尺度过程的间歇性和自相似性属性，是数据生成模型的重要参数估计方式。

散射矩在间歇过程分析中的应用

Intermittent process analysis with scattering moments

A public database system archiving a direct numerical simulation (DNS) data
set of isotropic, forced turbulence is described in this paper. The data set
consists of the DNS output on $1024^3$ spatial points and 1024 time-samples
spanning about one large-scale turn-over timescale. This complete $1024^4$
space-time history of turbulence is accessible to users remotely through an
interface that is based on the Web-services model. Users may write and execute
analysis programs on their host computers, while the programs make
subroutine-like calls that request desired parts of the data over the network.
The users are thus able to perform numerical experiments by accessing the 27
Terabytes of DNS data using regular platforms such as laptops. The architecture
of the database is explained, as are some of the locally defined functions,
such as differentiation and interpolation. Test calculations are performed to
illustrate the usage of the system and to verify the accuracy of the methods.
The database is then used to analyze a dynamical model for small-scale
intermittency in turbulence. Specifically, the dynamical effects of pressure
and viscous terms on the Lagrangian evolution of velocity increments are
evaluated using conditional averages calculated from the DNS data in the
database. It is shown that these effects differ considerably among themselves
and thus require different modeling strategies in Lagrangian models of velocity
increments and intermittency.

介绍了一个公共数据库系统，其中存档了一组与各向同性强制湍流有关的直接数值模拟数据（包括 $1024^3$ 空间点和 1024 时间样本），用户可以通过基于 Web 服务模型的界面远程访问这些数据并执行分析程序进行数字实验，该数据库用来分析与湍流中的小尺度间歇性有关的动力模型，具体地说，使用来自数据库中的 DNS 数据计算条件平均值来评估压力和粘性项对速度增量的 Lagrangian 演化的动态效应，并表明这些效应在它们之间存在显著差异，因此需要不同的建模策略。