Handling Uncertainties in Knowledge Modeling and Acquisition for the Development of a Knowledge‐Based System

Knowledge acquisition is perhaps the most important phase in the development of knowledge‐based systems (KBSs). Problems associated with knowledge acquisition include creating an explicit model of handling uncertainty for solving models in a complex domain. This article illustrates how knowledge modeling facilitates the acquisition of knowledge that is vague and uncertain. A hierarchical model is adopted for knowledge acquisition. The domain of the problem, i.e., damage assessment and vulnerability analysis of structures subjected to cyclones, is characterized by the presence of uncertainties in various forms. A KBS based on the hierarchical knowledge model has been developed that has the flexibility to handle the uncertainties using probabilistic and fuzzy set approaches depending on the nature of uncertainty. The hierarchical model for handling complexities and uncertainties in knowledge, the knowledge‐acquisition strategy, the inference mechanism, and the representation used are described. Two typical sessions, one for damage assessment and another for vulnerability analysis, are presented to demonstrate the working of the KBS and its efficacy in handling uncertain information.     

The possibilistic reliability theory: theoretical aspects and applications

The need to treat uncertainties in the design or assessment of structures today induces a lot of concerns in order to ensure the best security levels. This paper presents an original alternative to the probabilistic reliability theory, keeping the same features regarding some theoretical concepts (design points, reliability indexes) but highlighting easy implementations. The probabilistic or classical reliability theory is built on the principles of probability theory which introduces the probabilistic measure for evaluating confidence levels; the theory introduced in this paper is based on the possibility theory which uses a new confidence measure: the measure of possibility. While the probabilistic approach requires optimization of a multivariate function, the possibilistic approach reduces the study to the optimization of a variable function. Care is taken in explaining how to implement such a technique and for estimating distributions of possibility. Comparisons between the possibilistic and the probabilistic reliability theories are also given. Finally a section is dedicated to a concrete application: the reliability assessment of welded joints damaged by fatigue. This example provides a full application of the possibilistic reliability theory, from uncertainty modeling and possibility distribution estimation to failure possibility determinations.     

Reliability of corrosion-damaged steel structures using interval probability theory

Engineering decisions concerning the performance of existing structures must be made in the presence of uncertainties. The remaining capacity of corroded steel structures provides a good example of different aspects of uncertainty. These include: an unknown or partially known extent of damage; a variability in loading and an uncertain reserve of structural capacity depending on the mode of failure. The theory of structural reliability has been developed to provide a method of analysis for structural safety. In this paper, methods are proposed to compute the component reliability of corrosion-damaged steel members. The application of a recently developed theory called interval probability theory for system reliability is illustrated using the data obtained from actual samples of corroded beams.     

Probabilistic engineering analysis using the NESSUS software

The development of reliability-based design methods requires the use of general-purpose engineering analysis tools that predict the uncertainty in a response due to uncertainties in the model formulation and input parameters. Barriers that have prevented the full acceptance of probabilistic analysis methods in the engineering design community include availability of tools, ease of use, robust and accurate probabilistic analysis methods, and the ability to perform probabilistic analyses for large-scale problems. The goal of the reported work has been to develop a software tool that fully addresses these three aspects (availability, robustness and efficiency) to enable the designer to efficiently and accurately account for uncertainties as they might affect structural reliability and risk assessment. The paper discusses the NESSUS probabilistic engineering analysis software with specific sections on the reliability modeling and analysis process in NESSUS, the robust and accurate solution strategies incorporated in the available probabilistic analysis methods, and several application examples to demonstrate the applicability of probabilistic analysis to large-scale engineering problems.     

Safety analysis of structures with probability and evidence theory

In safety analysis of structures, classical probabilistic analysis has been a popular approach in engineering. However, it is not always to obtain sufficient information to model all uncertain parameters of structures system by probability theory, especially at early stage of design. Under this circumstance, probability theory (used to model random uncertainty) combined with evidence theory (used to model epistemic uncertainty) may be utilized in safety analysis of structures. This paper proposed a novel method for safety analysis of structures based on probability and evidence theory. Firstly, Bayes conversion method is used as the way for precision of evidence body, and the mean and variance of epistemic uncertain variables is defined. Then epistemic uncertainty variables is transformed to normal random variables by reflection transformation method, and the checking point method (J-C method) is used to solve most probability point and reliability. A numerical example and two engineering examples are given to demonstrate the performance of the proposed method. The results show both precision and computational efficiency of the method is high. Moreover, the proposed method provides basis for reliability-based optimization with the hybrid uncertainties.     

Fuzzy probabilistic optimisation of building performance

Fundamental performance criteria between action effects and relevant performance requirements for serviceability, safety, comfort and functionality are analyzed, assuming randomness of the effect action and both randomness and fuzziness of performance requirements. Randomness due to natural variability of basic variables is handled by commonly used probability theory methods, fuzziness due to vague or imprecise definitions of performance requirements is described by basic tools of the recently developed theory of fuzzy sets. Both types of uncertainties are combined in newly defined fuzzy probabilistic measures of building performance, damage function and fuzzy probability of performance failure, which are then analysed and applied similarly as conventional probabilistic quantities. An illustrative example of optimization of vibration constraints for building structures due to occupancy comfort indicates that commonly considered limiting values for acceleration may be uneconomical. However, theoretical models used to describe fuzzy probabilistic properties of performance requirements need to be reexamined using adequate experimental data.     

Role of slope reliability analysis in landslide risk management

Progress in the use of qualitative and quantitative methods of landslide risk assessment is briefly reviewed. The use of a hazard-consequence matrix approach is highlighted and attention is then restricted to aspects of hazard assessment in which formal reliability concepts can be used. Widely accepted geotechnical and geological models must form the basis of credible hazard assessments under different environmental conditions. However, conventional deterministic methods of geotechnical analysis need to be supplemented by studies within a probabilistic framework which takes into consideration parameter variability and other uncertainties. Suggestions are made for using the "reliability index" in preference to the "factor of safety" in comprehensive procedures for landslide risk management. Electronic Publication     

Time-dependent reliability assessment for mass concrete structures

Under the influences of random thermal creep stresses, the safety of mass concrete structures could be described by time-dependent reliability. In this paper, based on probabilistic finite element method (PFEM), numerical methods for the time-dependent reliability assessment are presented. By using the presented methods, various kinds of random variability including non-stationary temperature of concrete, modulus of elasticity, creep compliance and strength parameters of concrete can be conveniently taken into account. The suggested method is useful for the mass concrete structural design and safety evaluation when random factors should be taken into account.     

The effect of structural properties and ground motion variables on the global response of structural systems

The uncertainty in the seismic demand of a structure, corresponding to uncertainties in ground motion and in structural properties, needs to be properly characterised in a reliability analysis. In this study, the sensitivity of structural response to major uncertain variables is investigated using the variance-based method in order to determine which variables are most significant. The Sobol’ decomposition, based on a Monte Carlo simulation, is used to decompose the variance of the response into contributions from the individual ground motion and structural properties as input variables. The formulation of a dynamic structural response using the random-vibration theory, based only on the frequency information of the excitation, can provide an important basis for analytical sensitivity analysis of a structural response. The results show that the uncertainties in ground motion are more significant than uncertainties in structural properties for global structural response, especially peak roof displacement and maximum inter-storey drift.     

Formulation of Fuzzy Finite‐Element Methods for Solid Mechanics Problems

Accounting for uncertainties in mechanics problems has been accomplished previously by probabilistic methods that may require highly repetitive and time‐consuming computations to analyze the behavior of mathematical models. In addition to the repetitions, knowledge of the probability distribution of state variables is often incomplete. This article introduces a new treatment of uncertainties in continuum mechanics based on fuzzy set theory. Uncertainties or fuzzy numbers herein are viewed through the concept of presumption level of the uncertainty (α‐cut), α∈[0, 1]$, which gives an interval of confidence A_α = [a₁^(a), a₂^(α]. This treatment is included in a new fuzzy finite‐element formulation. The fuzzy approach to treating uncertainties in continuum mechanics is applied to load, geometric, and material uncertainties in a number of examples. Results demonstrate sharp inclusion of the fuzzy solutions in comparison with the exact solutions.     

Life-cycle cost optimal design of passive dissipative devices

The cost-effective performance of structures under natural hazards such as earthquakes and hurricanes has long been recognized to be an important topic in the design of civil engineering systems. A realistic comprehensive treatment of such a design requires proper integration of (i) methodologies for treating the uncertainties related to natural hazards and to the structural behavior over the entire life-cycle of the building, (ii) tools for evaluating the performance using socioeconomic criteria, as well as (iii) algorithms appropriate for stochastic analysis and optimization. A systematic probabilistic framework is presented here for detailed estimation and optimization of the life-cycle cost of engineering systems. This framework is a general one but the application of interest here is the design of passive dissipative devices for seismic risk mitigation. A comprehensive methodology is initially presented for earthquake loss estimation; this methodology uses the nonlinear time-history response of the structure under a given excitation to estimate the damage in a detailed, component level. A realistic probabilistic model is then presented for describing the ground motion time history for future earthquake excitations. In this setting, the life-cycle cost is uncertain and can be quantified by its expected value over the space of the uncertain parameters for the structural and excitation models. Because of the complexity of these models, calculation of this expected value is performed using stochastic simulation techniques. This approach, though, involves an unavoidable estimation error and significant computational cost, features which make efficient design optimization challenging. A highly efficient framework, consisting of two stages, is discussed for this stochastic optimization. An illustrative example is presented that shows the efficiency of the proposed methodology; it considers the seismic retrofitting of a four-story non-ductile reinforced-concrete building with viscous dampers.     

结构设计规范的可靠度设计方法质疑

讨论了建筑结构设计规范采用可靠度设计方法的缺陷与问题。结构设计规范面对复杂多样的结构群体 ,从统计数学观点出发的可靠度设计方法难以完整描述和概括这些结构设计中需要考虑的众多不确定性与不确知性。规范中的可靠度设计方法尚不成熟。目前 ,用多安全系数表达的设计方法可能更适用于各种结构的设计规范     

Probabilistic stability analysis of earth dam slope under transient seepage using multivariate adaptive regression splines

Earth dams are widespread throughout the world and their safety has gained increasing concern from geotechnical engineering societies. Although probabilistic stability analysis approach has been widely applied to the safety assessment of geotechnical structures, few studies have been performed to investigate the effects of water level fluctuations on earth dam slope stability considering uncertainties of soil parameters. This study proposes an efficient probabilistic stability analysis approach by integrating a soft computing algorithm of multivariate adaptive regression splines (MARS). The calibration of a MARS model generally requires a large number of training samples, which are obtained from repeated runs of deterministic seepage and slope stability analyses using the GeoStudio software. Based on the established MARS model, the earth dam slope failure probability can be conveniently evaluated. As an illustration, the proposed approach is applied to the probabilistic stability analysis of Ashigong earth dam under transient seepage. The effects of the uncertainties of soil parameters and water level fluctuation velocity on the earth dam slope failure probability are explored systematically. Results show that the MARS-based probabilistic stability analysis approach evaluates the earth slope failure probability with satisfactory accuracy and efficiency. The earth dam slope failure probability is significantly affected by the water level fluctuation velocity and the coefficient of variation of the effective friction angle.

     

Design certification with information-gap uncertainty

This paper presents a concept for formulating structural design-codes which is based on information-gap models of uncertainty rather than on probabilistic concepts. Info-gap models quantify uncertainty as the size of the gap between what is known and what could be known. Info-gap models of uncertainty are particularly useful when data on the uncertainties are quite limited. In the proposed procedure a design is certified if the robustness to failure from uncertain fluctuations exceeds a code-specified threshold. Design is thus based on immunity to uncertainty rather than on probability of survival. The key conclusion is that design-certification can exploit data about uncertainties without introducing probabilistic models. This is important when information is scarce, since verification of probabilistic models can then be difficult. Second, when partial probabilistic information is available, it can be incorporated in a hybrid info-gap/probabilistic analysis. Third, the proposed design certification incorporates recognition of the dual nature of uncertainty: that it may be pernicious but may also entail propitious possibilities. Examples are presented which illustrate the design procedure. The incorporation of partial probabilistic information is also demonstrated. The antagonism between the pernicious and propitious potentials of ambient uncertainty is illustrated.     

Reliability of prestressed concrete structures considering creep models

The reliability of prestressed concrete structures subject to viscoelastic behaviour is investigated regarding the creep model defined by the Eurocodes. A probabilistic phenomenological model is proposed for long-term creep strains on the basis of large database of creep tests. The uncertainties in the geometrical and mechanical parameters are modelled by random variables. The proposed model considers also the statistical fitting error in creep strain predictions. The reliability analysis is performed on a prestressed concrete deck, in order to show the large impact of time-dependent phenomena on the reliability of prestressed structures, and consequently the importance of considering appropriate viscoelastic models in the design of this kind of structures. Moreover, the errors related to creep models are shown to play a very important role in the structural safety assessment.     

Probabilistic modeling of structural deterioration of reinforced concrete beams under saline environment corrosion

For existing reinforced concrete structures exposed to saline or marine conditions, there is an increasing engineering interest in their remaining safety and serviceability. A significant factor is the corrosion of steel reinforcement. At present there is little field experience and other data available. This limits the possibility for developing purely empirical models for strength and performance deterioration for use in structural safety and serviceability assessment. An alternative approach using theoretical concepts and probabilistic modeling is proposed herein. It is based on the evidence that the rate of diffusion of chlorides is influenced by internal damage to the concrete surrounding the reinforcement. This may be due to localized stresses resulting from external loading or through concrete shrinkage. Usually, the net effect is that the time to initiation of active corrosion is shortened, leading to greater localized corrosion and earlier reduction of ultimate capacity and structural stiffness. The proposed procedure is applied to an example beam and compared to experimental observations, including estimates of uncertainty in the remaining ultimate moment capacity and beam stiffness. Reasonably good agreement between the results of the proposed procedure and the experiment was found.     

Reliability based analysis of the crosswind stability of railway vehicles

The computational models used to assess the crosswind stability of railway vehicles by multibody simulation (MBS) are affected by large uncertainties. Especially, the aerodynamic loads acting on the vehicle are difficult to model and the respective parameters cannot be easily acquired. Such uncertainties are usually neglected in the safety norms even though their effects on the risk assessment can be very large. In this paper the problem is tackled by modelling the most influential but uncertain parameters as stochastic variables. The resulting task can be efficiently managed by reliability techniques, mainly inherited from structural mechanics. This finally leads to the substitution of the conventional characteristic wind curve (CWC) by the probabilistic characteristic wind curve (PCWC). The proposed approach is referred to the most recent European norms for crosswind stability and exemplified on the test case of a German high speed train (ICE2).     

Probabilistic Evaluation of Structural Fire Resistance

The work described herein seeks to investigate a probabilistic framework to evaluate the fire resistance of structures given uncertainty in the fire load and structural resistance parameters. The methodology involves (i) the identification and characterization of uncertain parameters in the system, (ii) a stochastic analysis of the thermo-mechanical response of the structure, and (iii) the evaluation of structural reliability based on a suitable limit state function. The methodology is demonstrated through the analysis of a protected steel beam using Monte Carlo simulation with embedded finite element simulations. Model dimensionality is reduced using a response sensitivity analysis, and limit state functions are defined based on limiting deflection criteria used in fire resistance tests. Results demonstrate that the 1-h rated beam resists a natural fire exposure with a failure probability of less than ten percent, although additional discussion is warranted regarding what might be considered an acceptable level of risk in structural fire design. The study also demonstrates that probabilistic analysis of structural fire resistance provides an enhanced understanding of the factors affecting the resistance of structures to fire and offers a means for rationally improving structural designs to meet target performance objectives.     

建筑结构安全性理论的发展与应用

建筑结构安全性问题是建筑结构设计理论中的一项重要研究课题。本文简要地阐述了以统计数学为基础的近代建筑结构安全性理论的发展概况,提出以近似概率理论来改进我国现行的极限状态设计方法。文中结合我国办公楼楼面活荷载的统计分析结果,介绍了可变荷载的若干重要统计特性,还探讨了用新的结构安全度分析方法来确定分项安全系数的途径。本文综合地反映了我国近年来建筑结构安全性研究上的一些动态和成果。     

Influence of the exposure scenario and spatial correlation on the probabilistic life-cycle seismic performance of deteriorating RC frames

The probabilistic life-cycle seismic performance of reinforced concrete (RC) frames under chloride-induced corrosion is investigated considering the influence of the environmental aggressiveness and exposure scenario and the role of spatial correlation of the random variables. Chloride ingress and corrosion damage are described at cross-sectional level by two-dimensional concentration maps and damage indices. At the structural level, the seismic performance is evaluated in terms of lateral load response of the deteriorating structural system by means of time-variant non-linear analysis over the structural lifetime. The uncertainties involved in the problem are taken into account in probabilistic terms by Monte Carlo simulation. The procedure is applied to life-cycle assessment of a three-storey RC frame under different exposure scenarios, defined by varying both the concentration level and the spatial distribution of chlorides on the external surface of the columns, as well as different correlation levels of the random variables involved in the probabilistic analysis.