An interval finite element method for the analysis of structures with spatially varying uncertainties

Finite element analysis of linear-elastic structures with spatially varying uncertain properties is addressed within the framework of the interval model of uncertainty. Resorting to a recently proposed interval field model, the uncertain properties are expressed as the superposition of deterministic basis functions weighted by particular unitary intervals. An Interval Finite Element Method (IFEM) incorporating the interval field representation of uncertainties is formulated by applying an interval extension in conjunction with the standard energy approach. Uncertainty propagation analysis is performed by adopting a response surface approach which provides approximate explicit expressions of response bounds requiring only a few deterministic analyses. Then, the whole procedure is implemented in ABAQUS’ environment by coding User Subroutines and Python scripts. 2D plane stress and bending problems involving uncertain Young's modulus of the material are analyzed. The accuracy of the proposed IFEM as well as response variability under spatially dependent uncertainty are investigated

Recent advances on filtering and control for nonlinear stochastic complex systems with incomplete information: A survey

This Article is provided by the Brunel Open Access Publishing Fund - Copyright @ 2012 Hindawi PublishingSome recent advances on the filtering and control problems for nonlinear stochastic complex systems with incomplete information are surveyed. The incomplete information under consideration mainly includes missing measurements, randomly varying sensor delays, signal quantization, sensor saturations, and signal sampling. With such incomplete information, the developments on various filtering and control issues are reviewed in great detail. In particular, the addressed nonlinear stochastic complex systems are so comprehensive that they include conventional nonlinear stochastic systems, different kinds of complex networks, and a large class of sensor networks. The corresponding filtering and control technologies for such nonlinear stochastic complex systems are then discussed. Subsequently, some latest results on the filtering and control problems for the complex systems with incomplete information are given. Finally, conclusions are drawn and several possible future research directions are pointed out.This work was supported in part by the National Natural Science Foundation of China under Grant nos. 61134009, 61104125, 61028008, 61174136, 60974030, and 61074129, the Qing Lan Project of Jiangsu Province of China, the Project sponsored by SRF for ROCS of SEM of China, the Engineering and Physical Sciences Research Council EPSRC of the UK under Grant GR/S27658/01, the Royal Society of the UK, and the Alexander von Humboldt Foundation of Germany

Imprecise probabilistic evaluation of sewer flooding in urban drainage systems using random set theory

publication-status: Publishedtypes: ArticleCopyright © 2011 American Geophysical UnionUncertainty analysis is widely applied in water system modeling to quantify prediction uncertainty from models and data. Conventional methods typically handle various kinds of uncertainty using a single characterizing approach, be it probability theory or fuzzy set theory. However, using a single approach may not be appropriate, particularly when uncertainties are of different types. For example, in sewer flood estimation problems, random rainfall variables are used as model inputs and imprecise or subjective information is used to define model parameters. This paper presents a general framework for sewer flood estimation that enables simultaneous consideration of two types of uncertainty: randomness from rainfall data represented using imprecise probabilities and imprecision from model parameters represented by fuzzy numbers. These two types of uncertainties are combined using random set theory and then propagated through a hydrodynamic urban drainage model. Two propagation methods, i.e., discretization and Monte Carlo based methods, are presented and compared, with the latter shown to be much more computationally efficient and hence recommended for high-dimensional problems. The model output (flood depth) is generated in the form of lower and upper cumulative probabilities, which are best estimates given the various stochastic and epistemic uncertainties considered and which embrace the unknown true cumulative probability. The distance between the cumulative probabilities represents the extent of imprecise, incomplete, or conflicting information and can be reduced only when more knowledge is available. The proposed methodology has a more complete and thus more accurate representation of uncertainty in data and models and can effectively handle different uncertainty characterizations in a single, integrated framework for sewer flood estimation

Recent advances in intelligent-based structural health monitoring of civil structures

This survey paper deals with the structural health monitoring systems on the basis of methodologies involving intelligent techniques. The intelligent techniques are the most popular tools for damage identification in terms of high accuracy, reliable nature and the involvement of low cost. In this critical survey, a thorough analysis of various intelligent techniques is carried out considering the cases involved in civil structures. The importance and utilization of various intelligent tools to be mention as the concept of fuzzy logic, the technique of genetic algorithm, the methodology of neural network techniques, as well as the approaches of hybrid methods for the monitoring of the structural health of civil structures are illustrated in a sequential manner

Clouds, p-boxes, fuzzy sets, and other uncertainty representations in higher dimensions

Uncertainty modeling in real-life applications comprises some serious problems such as the curse of dimensionality and a lack of sufficient amount of statistical data. In this paper we give a survey of methods for uncertainty handling and elaborate the latest progress towards real-life applications with respect to the problems that come with it. We compare different methods and highlight their relationships. We introduce intuitively the concept of potential clouds, our latest approach which successfully copes with both higher dimensions and incomplete information

Measurements, Models, Systems and Design

531 s.

Towards development of fuzzy spatial datacubes : fundamental concepts with example for multidimensional coastal erosion risk assessment and representation

Les systèmes actuels de base de données géodécisionnels (GeoBI) ne tiennent généralement pas compte de l'incertitude liée à l'imprécision et le flou des objets; ils supposent que les objets ont une sémantique, une géométrie et une temporalité bien définies et précises. Un exemple de cela est la représentation des zones à risque par des polygones avec des limites bien définies. Ces polygones sont créés en utilisant des agrégations d'un ensemble d'unités spatiales définies sur soit des intérêts des organismes responsables ou les divisions de recensement national. Malgré la variation spatio-temporelle des multiples critères impliqués dans l’analyse du risque, chaque polygone a une valeur unique de risque attribué de façon homogène sur l'étendue du territoire. En réalité, la valeur du risque change progressivement d'un polygone à l'autre. Le passage d'une zone à l'autre n'est donc pas bien représenté avec les modèles d’objets bien définis (crisp). Cette thèse propose des concepts fondamentaux pour le développement d'une approche combinant le paradigme GeoBI et le concept flou de considérer la présence de l’incertitude spatiale dans la représentation des zones à risque. En fin de compte, nous supposons cela devrait améliorer l’analyse du risque. Pour ce faire, un cadre conceptuel est développé pour créer un model conceptuel d’une base de donnée multidimensionnelle avec une application pour l’analyse du risque d’érosion côtier. Ensuite, une approche de la représentation des risques fondée sur la logique floue est développée pour traiter l'incertitude spatiale inhérente liée à l'imprécision et le flou des objets. Pour cela, les fonctions d'appartenance floues sont définies en basant sur l’indice de vulnérabilité qui est un composant important du risque. Au lieu de déterminer les limites bien définies entre les zones à risque, l'approche proposée permet une transition en douceur d'une zone à une autre. Les valeurs d'appartenance de plusieurs indicateurs sont ensuite agrégées basées sur la formule des risques et les règles SI-ALORS de la logique floue pour représenter les zones à risque. Ensuite, les éléments clés d'un cube de données spatiales floues sont formalisés en combinant la théorie des ensembles flous et le paradigme de GeoBI. En plus, certains opérateurs d'agrégation spatiale floue sont présentés. En résumé, la principale contribution de cette thèse se réfère de la combinaison de la théorie des ensembles flous et le paradigme de GeoBI. Cela permet l’extraction de connaissances plus compréhensibles et appropriées avec le raisonnement humain à partir de données spatiales et non-spatiales. Pour ce faire, un cadre conceptuel a été proposé sur la base de paradigme GéoBI afin de développer un cube de données spatiale floue dans le system de Spatial Online Analytical Processing (SOLAP) pour évaluer le risque de l'érosion côtière. Cela nécessite d'abord d'élaborer un cadre pour concevoir le modèle conceptuel basé sur les paramètres de risque, d'autre part, de mettre en œuvre l’objet spatial flou dans une base de données spatiales multidimensionnelle, puis l'agrégation des objets spatiaux flous pour envisager à la représentation multi-échelle des zones à risque. Pour valider l'approche proposée, elle est appliquée à la région Perce (Est du Québec, Canada) comme une étude de cas.Current Geospatial Business Intelligence (GeoBI) systems typically do not take into account the uncertainty related to vagueness and fuzziness of objects; they assume that the objects have well-defined and exact semantics, geometry, and temporality. Representation of fuzzy zones by polygons with well-defined boundaries is an example of such approximation. This thesis uses an application in Coastal Erosion Risk Analysis (CERA) to illustrate the problems. CERA polygons are created using aggregations of a set of spatial units defined by either the stakeholders’ interests or national census divisions. Despite spatiotemporal variation of the multiple criteria involved in estimating the extent of coastal erosion risk, each polygon typically has a unique value of risk attributed homogeneously across its spatial extent. In reality, risk value changes gradually within polygons and when going from one polygon to another. Therefore, the transition from one zone to another is not properly represented with crisp object models. The main objective of the present thesis is to develop a new approach combining GeoBI paradigm and fuzzy concept to consider the presence of the spatial uncertainty in the representation of risk zones. Ultimately, we assume this should improve coastal erosion risk assessment. To do so, a comprehensive GeoBI-based conceptual framework is developed with an application for Coastal Erosion Risk Assessment (CERA). Then, a fuzzy-based risk representation approach is developed to handle the inherent spatial uncertainty related to vagueness and fuzziness of objects. Fuzzy membership functions are defined by an expert-based vulnerability index. Instead of determining well-defined boundaries between risk zones, the proposed approach permits a smooth transition from one zone to another. The membership values of multiple indicators (e.g. slop and elevation of region under study, infrastructures, houses, hydrology network and so on) are then aggregated based on risk formula and Fuzzy IF-THEN rules to represent risk zones. Also, the key elements of a fuzzy spatial datacube are formally defined by combining fuzzy set theory and GeoBI paradigm. In this regard, some operators of fuzzy spatial aggregation are also formally defined. The main contribution of this study is combining fuzzy set theory and GeoBI. This makes spatial knowledge discovery more understandable with human reasoning and perception. Hence, an analytical conceptual framework was proposed based on GeoBI paradigm to develop a fuzzy spatial datacube within Spatial Online Analytical Processing (SOLAP) to assess coastal erosion risk. This necessitates developing a framework to design a conceptual model based on risk parameters, implementing fuzzy spatial objects in a spatial multi-dimensional database, and aggregating fuzzy spatial objects to deal with multi-scale representation of risk zones. To validate the proposed approach, it is applied to Perce region (Eastern Quebec, Canada) as a case study

A Spatial Fuzzy Compromise Approach for Flood Disaster Management

Natural disasters affect regions with different intensity and produce damages that vary in space. Topographical features of the region; location of properties that may be exposed to the peril; level of exposure; impact of different mitigation measures; are all variables with considerable spatial variability. A new method for evaluation of disaster impacts has been presented in this report that takes into consideration spatial variability of variables involved and associated uncertainty. Flood management has been used to illustrate the utility of proposed approach. Floodplain management is a spatial problem. Representation of flood damage mitigation alternatives and objectives in space provides a better insight into the management problem and its characteristics. Protection of a region from floods can be achieved through various structural and non-structural measures. Comparison of different measures and evaluation of their impacts is based on the multiple criteria. If they are described spatially, decision-making problem can be conceptualized as spatial multi criteria decision-making (MCDM). Tkach and Simonovic (1997) introduced spatial Compromise Programming (SPC) technique to account for spatial variability in flood management. Some of the criteria and preferences of the stakeholders involved with flood management are subject to uncertainty that may originate in the data, knowledge of the domain or our ability to adequately describe the decision problem. The main characteristic of flood management is the existence of objective and subjective uncertainty. Fuzzy set theory has been successfully used to address both, objective and subjective uncertainty. Bender and Simonovic (2000) incorporated vagueness and imprecision as sources of uncertainty into multi criteria decision-making in water resources. In this report a new technique named Spatial Fuzzy Compromise Programming (SFCP) has been developed to enhance our ability to address the issues related to uncertainties in spatial environment. A general fuzzy compromise programming technique, when made 2 spatially distributed, proved to be a powerful and flexible addition to the list of techniques available for decision making where multiple criteria are used to judge multiple alternatives. All uncertain variables (subjective and objective) are modeled by way of fuzzy sets. In the present study, fuzzy measures have been introduced to spatial multi criteria decision-making in the GIS environment in order to account for uncertainties. Through a case study of the Red River floodplain near the City of St. Adolphe in Manitoba, Canada, it has been illustrated that the new technique provides measurable improvement in flood management. Final results in the form of maps that shown spatial distribution of the impacts of mitigation measures on the region can be of great value to insurance industry.https://ir.lib.uwo.ca/wrrr/1004/thumbnail.jp

Risk-informed decision-making in the presence of epistemic uncertainty

International audienceAn important issue in risk analysis is the distinction between epistemic and aleatory uncertainties. In this paper, the use of distinct representation formats for aleatory and epistemic uncertainties is advocated, the latter being modelled by sets of possible values. Modern uncertainty theories based on convex sets of probabilities are known to be instrumental for hybrid representations where aleatory and epistemic components of uncertainty remain distinct. Simple uncertainty representation techniques based on fuzzy intervals and p-boxes are used in practice. This paper outlines a risk analysis methodology from elicitation of knowledge about parameters to decision. It proposes an elicitation methodology where the chosen representation format depends on the nature and the amount of available information. Uncertainty propagation methods then blend Monte-Carlo simulation and interval analysis techniques. Nevertheless, results provided by these techniques, often in terms of probability intervals, may be too complex to interpret for a decision-maker and we therefore propose to compute a unique indicator of the likelihood of risk, called confidence index. It explicitly accounts for the decision-maker's attitude in the face of ambiguity. This step takes place at the end of the risk analysis process, when no further collection of evidence is possible that might reduce the ambiguity due to epistemic uncertainty. This last feature stands in contrast with the Bayesian methodology, where epistemic uncertainties on input parameters are modelled by single subjective probabilities at the beginning of the risk analysis process