Meta-models for structural reliability and uncertainty quantification

A meta-model (or a surrogate model) is the modern name for what was traditionally called a response surface. It is intended to mimic the behaviour of a computational model M (e.g. a finite element model in mechanics) while being inexpensive to evaluate, in contrast to the original model which may take hours or even days of computer processing time. In this paper various types of meta-models that have been used in the last decade in the context of structural reliability are reviewed. More specifically classical polynomial response surfaces, polynomial chaos expansions and kriging are addressed. It is shown how the need for error estimates and adaptivity in their construction has brought this type of approaches to a high level of efficiency. A new technique that solves the problem of the potential biasedness in the estimation of a probability of failure through the use of meta-models is finally presented.Comment: Keynote lecture Fifth Asian-Pacific Symposium on Structural Reliability and its Applications (5th APSSRA) May 2012, Singapor

Polynomial-Chaos-based Kriging

Computer simulation has become the standard tool in many engineering fields for designing and optimizing systems, as well as for assessing their reliability. To cope with demanding analysis such as optimization and reliability, surrogate models (a.k.a meta-models) have been increasingly investigated in the last decade. Polynomial Chaos Expansions (PCE) and Kriging are two popular non-intrusive meta-modelling techniques. PCE surrogates the computational model with a series of orthonormal polynomials in the input variables where polynomials are chosen in coherency with the probability distributions of those input variables. On the other hand, Kriging assumes that the computer model behaves as a realization of a Gaussian random process whose parameters are estimated from the available computer runs, i.e. input vectors and response values. These two techniques have been developed more or less in parallel so far with little interaction between the researchers in the two fields. In this paper, PC-Kriging is derived as a new non-intrusive meta-modeling approach combining PCE and Kriging. A sparse set of orthonormal polynomials (PCE) approximates the global behavior of the computational model whereas Kriging manages the local variability of the model output. An adaptive algorithm similar to the least angle regression algorithm determines the optimal sparse set of polynomials. PC-Kriging is validated on various benchmark analytical functions which are easy to sample for reference results. From the numerical investigations it is concluded that PC-Kriging performs better than or at least as good as the two distinct meta-modeling techniques. A larger gain in accuracy is obtained when the experimental design has a limited size, which is an asset when dealing with demanding computational models

Dysfunctional Social Reinforcement Processing in Disruptive Behavior Disorders: An Functional Magnetic Resonance Imaging Study.

ObjectivePrior functional magnetic resonance imaging (fMRI) work has revealed that children/adolescents with disruptive behavior disorders (DBDs) show dysfunctional reward/non-reward processing of non-social reinforcements in the context of instrumental learning tasks. Neural responsiveness to social reinforcements during instrumental learning, despite the importance of this for socialization, has not yet been previously investigated.MethodsTwenty-nine healthy children/adolescents and 19 children/adolescents with DBDs performed the fMRI social/non-social reinforcement learning task. Participants responded to random fractal image stimuli and received social and non-social rewards/non-rewards according to their accuracy.ResultsChildren/adolescents with DBDs showed significantly reduced responses within the caudate and posterior cingulate cortex (PCC) to non-social (financial) rewards and social non-rewards (the distress of others). Connectivity analyses revealed that children/adolescents with DBDs have decreased positive functional connectivity between the ventral striatum (VST) and the ventromedial prefrontal cortex (vmPFC) seeds and the lateral frontal cortex in response to reward relative to non-reward, irrespective of its sociality. In addition, they showed decreased positive connectivity between the vmPFC seed and the amygdala in response to non-reward relative to reward.ConclusionThese data indicate compromised reinforcement processing of both non-social rewards and social non-rewards in children/adolescents with DBDs within core regions for instrumental learning and reinforcement-based decision- making (caudate and PCC). In addition, children/adolescents with DBDs show dysfunctional interactions between the VST, vmPFC, and lateral frontal cortex in response to rewarded instrumental actions potentially reflecting disruptions in attention to rewarded stimuli

Application of Computational Intelligence Techniques to Process Industry Problems

In the last two decades there has been a large progress in the computational intelligence research field. The fruits of the effort spent on the research in the discussed field are powerful techniques for pattern recognition, data mining, data modelling, etc. These techniques achieve high performance on traditional data sets like the UCI machine learning database. Unfortunately, this kind of data sources usually represent clean data without any problems like data outliers, missing values, feature co-linearity, etc. common to real-life industrial data. The presence of faulty data samples can have very harmful effects on the models, for example if presented during the training of the models, it can either cause sub-optimal performance of the trained model or in the worst case destroy the so far learnt knowledge of the model. For these reasons the application of present modelling techniques to industrial problems has developed into a research field on its own. Based on the discussion of the properties and issues of the data and the state-of-the-art modelling techniques in the process industry, in this paper a novel unified approach to the development of predictive models in the process industry is presented

Human capital and entrepreneurial success : a meta-analytical review

The study meta-analytically integrates results from three decades of human capital research in entrepreneurship. Based on 70 independent samples (N = 24,733), we found a significant but small relationship between human capital and success (r(c) = .098). We examined theoretically derived moderators of this relationship referring to conceptualizations of human capital, to context, and to measurement of success. The relationship was higher for outcomes of human capital investments (knowledge/skills) than for human capital investments (education/experience), for human capital with high task-relatedness compared to low task-relatedness, for young businesses compared to old businesses, and for the dependent variable size compared to growth or profitability. Findings are relevant for practitioners (lenders, policy makers, educators) and for future research. Our findings show that future research should pursue moderator approaches to study the effects of human capital on success. Further, human capital is most important if it is task-related and if it consists of outcomes of human capital investments rather than human capital investments; this suggests that research should overcome a static view of human capital and should rather investigate the processes of learning, knowledge acquisition, and the transfer of knowledge to entrepreneurial tasks

Mechanism Deduction from Noisy Chemical Reaction Networks

We introduce KiNetX, a fully automated meta-algorithm for the kinetic analysis of complex chemical reaction networks derived from semi-accurate but efficient electronic structure calculations. It is designed to (i) accelerate the automated exploration of such networks, and (ii) cope with model-inherent errors in electronic structure calculations on elementary reaction steps. We developed and implemented KiNetX to possess three features. First, KiNetX evaluates the kinetic relevance of every species in a (yet incomplete) reaction network to confine the search for new elementary reaction steps only to those species that are considered possibly relevant. Second, KiNetX identifies and eliminates all kinetically irrelevant species and elementary reactions to reduce a complex network graph to a comprehensible mechanism. Third, KiNetX estimates the sensitivity of species concentrations toward changes in individual rate constants (derived from relative free energies), which allows us to systematically select the most efficient electronic structure model for each elementary reaction given a predefined accuracy. The novelty of KiNetX consists in the rigorous propagation of correlated free-energy uncertainty through all steps of our kinetic analyis. To examine the performance of KiNetX, we developed AutoNetGen. It semirandomly generates chemistry-mimicking reaction networks by encoding chemical logic into their underlying graph structure. AutoNetGen allows us to consider a vast number of distinct chemistry-like scenarios and, hence, to discuss assess the importance of rigorous uncertainty propagation in a statistical context. Our results reveal that KiNetX reliably supports the deduction of product ratios, dominant reaction pathways, and possibly other network properties from semi-accurate electronic structure data.Comment: 36 pages, 4 figures, 2 table