Vibration and stress analysis in the presence of structural uncertainty

At medium to high frequencies the dynamic response of a built-up engineering system, such as an automobile, can be sensitive to small random manufacturing imperfections. Ideally the statistics of the system response in the presence of these uncertainties should be computed at the design stage, but in practice this is an extremely difficult task. In this paper a brief review of the methods available for the analysis of systems with uncertainty is presented, and attention is then focused on two particular "non- parametric" methods: statistical energy analysis (SEA), and the hybrid method. The main governing equations are presented, and a number of example applications are considered, ranging from academic benchmark studies to industrial design studies. © 2009 IOP Publishing Ltd.

Handling uncertainty in housing stock models

Housing stock models can be useful tools in helping to assess the environmental and socio-economic impacts of retrofits to residential buildings; however, existing housing stock models are not able to quantify the uncertainties that arise in the modelling process from various sources, thus limiting the role that they can play in helping decision makers. This paper examines the different sources of uncertainty involved in housing stock models and proposes a framework for handling these uncertainties. This framework involves integrating probabilistic sensitivity analysis with a Bayesian calibration process in order to quantify uncertain parameters more accurately. The proposed framework is tested on a case study building, and suggestions are made on how to expand the framework for retrofit analysis at an urban-scale. © 2011 Elsevier Ltd.

Modelling the evolution of uncertainty levels during design

Design work involves uncertainty that arises from, and influences, the progressive development of solutions. This paper analyses the influences of evolving uncertainty levels on the design process. We focus on uncertainties associated with choosing the values of design parameters, and do not consider in detail the issues that arise when parameters must first be identified. Aspects of uncertainty and its evolution are discussed, and a new task-based model is introduced to describe process behaviour in terms of changing uncertainty levels. The model is applied to study two process configuration problems based on aircraft wing design: one using an analytical solution and one using Monte-Carlo simulation. The applications show that modelling uncertainty levels during design can help assess management policies, such as how many concepts should be considered during design and to what level of accuracy. © 2011 Springer-Verlag.

Strength mobilization in clays and silts

A large database of 115 triaxial, direct simple shear, and cyclic tests on 19 clays and silts is presented and analysed to develop an empirical framework for the prediction of the mobilization of the undrained shear strength, cu, of natural clays tested from an initially isotropic state of stress. The strain at half the peak undrained strength (γM=2) is used to normalize the shear strain data between mobilized strengths of 0.2cu and 0.8cu. A power law with an exponent of 0.6 is found to describe all the normalized data within a strain factor of 1.75 when a representative sample provides a value for γM=2. Multi-linear regression analysis shows that γM=2 is a function of cu, plasticity index Ip, and initial mean effective stress p′0. Of the 97 stress-strain curves for which cu, Ip, and p′0 were available, the observed values of γM=2 fell within a factor of three of the regression; this additional uncertainty should be acknowledged if a designer wished to limit immediate foundation settlements on the basis of an undrained strength profile and the plasticity index of the clay. The influence of stress history is also discussed. The application of these stress-strain relations to serviceability design calculations is portrayed through a worked example. The implications for geotechnical decision-making and codes of practice are considered.

Modulation of pain ratings by expectation and uncertainty: Behavioral characteristics and anticipatory neural correlates.

Expectations about the magnitude of impending pain exert a substantial effect on subsequent perception. However, the neural mechanisms that underlie the predictive processes that modulate pain are poorly understood. In a combined behavioral and high-density electrophysiological study we measured anticipatory neural responses to heat stimuli to determine how predictions of pain intensity, and certainty about those predictions, modulate brain activity and subjective pain ratings. Prior to receiving randomized laser heat stimuli at different intensities (low, medium or high) subjects (n=15) viewed cues that either accurately informed them of forthcoming intensity (certain expectation) or not (uncertain expectation). Pain ratings were biased towards prior expectations of either high or low intensity. Anticipatory neural responses increased with expectations of painful vs. non-painful heat intensity, suggesting the presence of neural responses that represent predicted heat stimulus intensity. These anticipatory responses also correlated with the amplitude of the Laser-Evoked Potential (LEP) response to painful stimuli when the intensity was predictable. Source analysis (LORETA) revealed that uncertainty about expected heat intensity involves an anticipatory cortical network commonly associated with attention (left dorsolateral prefrontal, posterior cingulate and bilateral inferior parietal cortices). Relative certainty, however, involves cortical areas previously associated with semantic and prospective memory (left inferior frontal and inferior temporal cortex, and right anterior prefrontal cortex). This suggests that biasing of pain reports and LEPs by expectation involves temporally precise activity in specific cortical networks.

Coupling model uncertainty for coupled rainfall/runoff and surface water quality models in river problems

Coupled hydrology and water quality models are an important tool today, used in the understanding and management of surface water and watershed areas. Such problems are generally subject to substantial uncertainty in parameters, process understanding, and data. Component models, drawing on different data, concepts, and structures, are affected differently by each of these uncertain elements. This paper proposes a framework wherein the response of component models to their respective uncertain elements can be quantified and assessed, using a hydrological model and water quality model as two exemplars. The resulting assessments can be used to identify model coupling strategies that permit more appropriate use and calibration of individual models, and a better overall coupled model response. One key finding was that an approximate balance of water quality and hydrological model responses can be obtained using both the QUAL2E and Mike11 water quality models. The balance point, however, does not support a particularly narrow surface response (or stringent calibration criteria) with respect to the water quality calibration data, at least in the case examined here. Additionally, it is clear from the results presented that the structural source of uncertainty is at least as significant as parameter-based uncertainties in areal models. © 2012 John Wiley & Sons, Ltd.

Efficient parametric uncertainty analysis within the hybrid Finite Element/Statistical Energy Analysis method

This paper is concerned with the development of efficient algorithms for propagating parametric uncertainty within the context of the hybrid Finite Element/Statistical Energy Analysis (FE/SEA) approach to the analysis of complex vibro-acoustic systems. This approach models the system as a combination of SEA subsystems and FE components; it is assumed that the FE components have fully deterministic properties, while the SEA subsystems have a high degree of randomness. The method has been recently generalised by allowing the FE components to possess parametric uncertainty, leading to two ensembles of uncertainty: a non-parametric one (SEA subsystems) and a parametric one (FE components). The SEA subsystems ensemble is dealt with analytically, while the effect of the additional FE components ensemble can be dealt with by Monte Carlo Simulations. However, this approach can be computationally intensive when applied to complex engineering systems having many uncertain parameters. Two different strategies are proposed: (i) the combination of the hybrid FE/SEA method with the First Order Reliability Method which allows the probability of the non-parametric ensemble average of a response variable exceeding a barrier to be calculated and (ii) the combination of the hybrid FE/SEA method with Laplace's method which allows the evaluation of the probability of a response variable exceeding a limit value. The proposed approaches are illustrated using two built-up plate systems with uncertain properties and the results are validated against direct integration, Monte Carlo simulations of the FE and of the hybrid FE/SEA models. © 2013 Elsevier Ltd.

Bayesian parameter identification for vibro-acoustic models with nonparametric uncertainty

Vibration and acoustic analysis at higher frequencies faces two challenges: computing the response without using an excessive number of degrees of freedom, and quantifying its uncertainty due to small spatial variations in geometry, material properties and boundary conditions. Efficient models make use of the observation that when the response of a decoupled vibro-acoustic subsystem is sufficiently sensitive to uncertainty in such spatial variations, the local statistics of its natural frequencies and mode shapes saturate to universal probability distributions. This holds irrespective of the causes that underly these spatial variations and thus leads to a nonparametric description of uncertainty. This work deals with the identification of uncertain parameters in such models by using experimental data. One of the difficulties is that both experimental errors and modeling errors, due to the nonparametric uncertainty that is inherent to the model type, are present. This is tackled by employing a Bayesian inference strategy. The prior probability distribution of the uncertain parameters is constructed using the maximum entropy principle. The likelihood function that is subsequently computed takes the experimental information, the experimental errors and the modeling errors into account. The posterior probability distribution, which is computed with the Markov Chain Monte Carlo method, provides a full uncertainty quantification of the identified parameters, and indicates how well their uncertainty is reduced, with respect to the prior information, by the experimental data. © 2013 Taylor & Francis Group, London.