Reducing Uncertainty in Aeroelastic Flutter Boundaries Using Experimental Data

Flutter prediction as currently practiced is usually deterministic, with a single structural model used to represent an aircraft. By using interval analysis to take into account structural variability, recent work has demonstrated that small changes in the structure can lead to very large changes in the altitude at which
utter occurs (Marques, Badcock, et al., J. Aircraft, 2010). In this follow-up work we examine the same phenomenon using probabilistic collocation (PC), an uncertainty quantification technique which can eficiently propagate multivariate stochastic input through a simulation code,
in this case an eigenvalue-based fluid-structure stability code. The resulting analysis predicts the consequences of an uncertain structure on incidence of
utter in probabilistic terms { information that could be useful in planning
flight-tests and assessing the risk of structural failure. The uncertainty in
utter altitude is confirmed to be substantial. Assuming that the structural uncertainty represents a epistemic uncertainty regarding the
structure, it may be reduced with the availability of additional information { for example aeroelastic response data from a flight-test. Such data is used to update the structural uncertainty using Bayes' theorem. The consequent
utter uncertainty is significantly reduced across the entire Mach number range.

Modeling Multivariate Interest Rates Using Time-Varying Copulas and Reducible Nonlinear Stochastic Differential Equations

We propose a new approach for modeling nonlinear multivariate interest rate processes based on time-varying copulas and reducible stochastic differential equations (SDEs). In the modeling of the marginal processes, we consider a class of nonlinear SDEs that are reducible to Ornstein--Uhlenbeck (OU) process or Cox, Ingersoll, and Ross (1985) (CIR) process. The reducibility is achieved via a nonlinear transformation function. The main advantage of this approach is that these SDEs can account for nonlinear features, observed in short-term interest rate series, while at the same time leading to exact discretization and closed-form likelihood functions. Although a rich set of specifications may be entertained, our exposition focuses on a couple of nonlinear constant elasticity volatility (CEV) processes, denoted as OU-CEV and CIR-CEV, respectively. These two processes encompass a number of existing models that have closed-form likelihood functions. The transition density, the conditional distribution function, and the steady-state density function are derived in closed form as well as the conditional and unconditional moments for both processes. In order to obtain a more flexible functional form over time, we allow the transformation function to be time varying. Results from our study of U.S. and UK short-term interest rates suggest that the new models outperform existing parametric models with closed-form likelihood functions. We also find the time-varying effects in the transformation functions statistically significant. To examine the joint behavior of interest rate series, we propose flexible nonlinear multivariate models by joining univariate nonlinear processes via appropriate copulas. We study the conditional dependence structure of the two rates using Patton (2006a) time-varying symmetrized Joe--Clayton copula. We find evidence of asymmetric dependence between the two rates, and that the level of dependence is positively related to the level of the two rates. (JEL: C13, C32, G12) Copyright The Author 2010. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org, Oxford University Press.

Improved fault diagnosis in multivariate systems using regression-based reconstruction

Subspace monitoring has recently been proposed as a condition monitoring tool that requires considerably fewer variables to be analysed compared to dynamic principal component analysis (PCA). This paper analyses subspace monitoring in identifying and isolating fault conditions, which reveals that the existing work suffers from inherent limitations if complex fault senarios arise. Based on the assumption that the fault signature is deterministic while the monitored variables are stochastic, the paper introduces a regression-based reconstruction technique to overcome these limitations. The utility of the proposed fault identification and isolation method is shown using a simulation example and the analysis of experimental data from an industrial reactive distillation unit.

Relative role of deterministic and stochastic determinants of soil animal community: a spatially explicit analysis of oribatid mites

1. Ecologists are debating the relative role of deterministic and stochastic determinants of community structure. Although the high diversity and strong spatial structure of soil animal assemblages could provide ecologists with an ideal ecological scenario, surprisingly little information is available on these assemblages.
2. We studied species-rich soil oribatid mite assemblages from a Mediterranean beech forest and a grassland. We applied multivariate regression approaches and analysed spatial autocorrelation at multiple spatial scales using Moran's eigenvectors. Results were used to partition community variance in terms of the amount of variation uniquely accounted for by environmental correlates (e.g. organic matter) and geographical position. Estimated neutral diversity and immigration parameters were also applied to a soil animal group for the first time to simulate patterns of community dissimilarity expected under neutrality, thereby testing neutral predictions.
3. After accounting for spatial autocorrelation, the correlation between community structure and key environmental parameters disappeared: about 40% of community variation consisted of spatial patterns independent of measured environmental variables such as organic matter. Environmentally independent spatial patterns encompassed the entire range of scales accounted for by the sampling design (from tens of cm to 100 m). This spatial variation could be due to either unmeasured but spatially structured variables or stochastic drift mediated by dispersal. Observed levels of community dissimilarity were significantly different from those predicted by neutral models.
4. Oribatid mite assemblages are dominated by processes involving both deterministic and stochastic components and operating at multiple scales. Spatial patterns independent of the measured environmental variables are a prominent feature of the targeted assemblages, but patterns of community dissimilarity do not match neutral predictions. This suggests that either niche-mediated competition or environmental filtering or both are contributing to the core structure of the community. This study indicates new lines of investigation for understanding the mechanisms that determine the signature of the deterministic component of animal community assembly.

Fault Diagnosis in Internal Combustion Engines Using Nonlinear Multivariate Statistics

This paper presents a statistical-based fault diagnosis scheme for application to internal combustion engines. The scheme relies on an identified model that describes the relationships between a set of recorded engine variables using principal component analysis (PCA). Since combustion cycles are complex in nature and produce nonlinear relationships between the recorded engine variables, the paper proposes the use of nonlinear PCA (NLPCA). The paper further justifies the use of NLPCA by comparing the model accuracy of the NLPCA model with that of a linear PCA model. A new nonlinear variable reconstruction algorithm and bivariate scatter plots are proposed for fault isolation, following the application of NLPCA. The proposed technique allows the diagnosis of different fault types under steady-state operating conditions. More precisely, nonlinear variable reconstruction can remove the fault signature from the recorded engine data, which allows the identification and isolation of the root cause of abnormal engine behaviour. The paper shows that this can lead to (i) an enhanced identification of potential root causes of abnormal events and (ii) the masking of faulty sensor readings. The effectiveness of the enhanced NLPCA based monitoring scheme is illustrated by its application to a sensor fault and a process fault. The sensor fault relates to a drift in the fuel flow reading, whilst the process fault relates to a partial blockage of the intercooler. These faults are introduced to a Volkswagen TDI 1.9 Litre diesel engine mounted on an experimental engine test bench facility.

Dynamic Multivariate Statistical Process Control using Subspace Identification

This paper points out a serious flaw in dynamic multivariate statistical process control (MSPC). The principal component analysis of a linear time series model that is employed to capture auto- and cross-correlation in recorded data may produce a considerable number of variables to be analysed. To give a dynamic representation of the data (based on variable correlation) and circumvent the production of a large time-series structure, a linear state space model is used here instead. The paper demonstrates that incorporating a state space model, the number of variables to be analysed dynamically can be considerably reduced, compared to conventional dynamic MSPC techniques.

Statistical Monitoring of Dynamic Multivariate Processes: Part I: Modeling Auto- and Cross-Correlation

The work in this paper is of particular significance since it considers the problem of modelling cross- and auto-correlation in statistical process monitoring. The presence of both types of correlation can lead to fault insensitivity or false alarms, although in published literature to date, only autocorrelation has been broadly considered. The proposed method, which uses a Kalman innovation model, effectively removes both correlations. The paper (and Part 2 [2]) has emerged from work supported by EPSRC grant GR/S84354/01 and is of direct relevance to problems in several application areas including chemical, electrical, and mechanical process monitoring.

Statistical Monitoring of Dynamic Multivariate Processes: Part II: Identifying Fault Magnitude and Signature

This paper builds on work presented in the first paper, Part 1 [1] and is of equal significance. The paper proposes a novel compensation method to preserve the integrity of step-fault signatures prevalent in various processes that can be masked during the removal of both auto- and cross correlation. Using industrial data, the paper demonstrates the benefit of the proposed method, which is applicable to chemical, electrical, and mechanical process monitoring. This paper, (and Part 1 [1]), has led to further work supported by EPSRC grant GR/S84354/01 involving kernel PCA methods.

Multivariate prediction of clarified butter composition using Raman spectroscopy

Raman spectroscopy has been used to predict the abundance of the FA in clarified butterfat that was obtained from dairy cows fed a range of levels of rapeseed oil in their diet. Partial least squares regression of the Raman spectra against FA compositions obtained by GC showed good prediction for the five major (abundance >5%) FA with R-2=0.74-0.92 and a root mean SE of prediction (RMSEP) that was 5-7% of the mean. In general, the prediction accuracy fell with decreasing abundance in the sample, but the RMSEP was 1.25%. The Raman method has the best prediction ability for unsaturated FA (R-2=0.85-0.92), and in particular trans unsaturated FA (best-predicted FA was 18:1 tDelta9). This enhancement was attributed to the isolation of the unsaturated modes from the saturated modes and the significantly higher spectral response of unsaturated bonds compared with saturated bonds. Raman spectra of the melted butter samples could also be used to predict bulk parameters calculated from standard analyzes, such as iodine value (R-2=0.80) and solid fat content at low temperature (R-2=0.87). For solid fat contents determined at higher temperatures, the prediction ability was significantly reduced (R-2=0.42), and this decrease in performance was attributed to the smaller range of values in solid fat content at the higher temperatures. Finally, although the prediction errors for the abundances of each of the FA in a given sample are much larger with Raman than with full GC analysis, the accuracy is acceptably high for quality control applications. This, combined with the fact that Raman spectra can be obtained with no sample preparation and with 60-s data collection times, means that high-throughput, on-line Raman analysis of butter samples should be possible.

Analytical description of stochastic field-Line wandering in magnetic turbulence

A nonperturbative nonlinear statistical approach is presented to describe turbulent magnetic systems embedded in a uniform mean magnetic field. A general formula in the form of an ordinary differential equation for magnetic field-line wandering (random walk) is derived. By considering the solution of this equation for different limits several new results are obtained. As an example, it is demonstrated that the stochastic wandering of magnetic field-lines in a two-component turbulence model leads to superdiffusive transport, contrary to an existing diffusive picture. The validity of quasilinear theory for field-line wandering is discussed, with respect to different turbulence geometry models, and previous diffusive results are shown to be deduced in appropriate limits.