Probabilistic Seismic Demand Analysis of Structures Using Reliability Approaches

In practical engineering design, most data sets for system uncertainties are insufficiently sampled from un- known statistical distributions, known as epistemic uncer- tainty. Existing methods in uncertainty-based design optimization have difficulty in handling both aleatory and epistemic uncertainties. To tackle design problems engaging both epistemic and aleatory uncertainties, reliability-based design optimization (RBDO) is integrated with Bayes theorem. It is referred to as Bayesian RBDO. However, Bayesian RBDO becomes extremely expensive when employing the first- or second-order reliability method (FORM/SORM) for reliability predictions. Thus, this paper proposes development of Bayesian RBDO methodology and its integration to a numerical solver, the eigenvector dimension reduction (EDR) method, for Bayesian reliabil- ity analysis. The EDR method takes a sensitivity-free approach for reliability analysis so that it is very efficient and accurate compared with other reliability methods such as FORM/SORM. Efficiency and accuracy of the Bayesian RBDO process are substantially improved after this integration.

Risk plays an important role in the decision making process. To assess the severity and likelihood of impairment to human health from exposure to a substance or activity that under plausible circumstances can cause harm to human health is the main purpose of risk assessment. It is important to know the nature and characteristic of all available information, data or model parameters which are more generally tainted with aleatory and epistemic uncertainty or both type of uncertainty. In some situation, model parameters are affected by aleatory uncertainty and simultaneously other some parameters are affected by epistemic uncertainty, how far computation of the risk is concern, two ways to deal with the situation either transform all the uncertainties to one type of format or need for joint propagation of uncertainties. In this paper, an effort has been made to combine probability distributions, generalized fuzzy numbers, normal fuzzy numbers and generalized interval valued fuzzy numbers within the same framework.

A novel method for importance measure analysis in the presence of epistemic and aleatory uncertainties

The design of engineering systems is often based on analysis models with substantial errors in predicting failures, that is epistemic uncertainty. The epistemic uncertainty is reduced by post design tests, and the safety of unsafe designs restored by redesign. When this process of design, test and redesign is to be based on probabilistic analysis, there is some controversy on whether uncertainty associated with variability (aleatory uncertainty) should be treated differently than the epistemic uncertainty. In this paper we compare several approaches to design and redesign and treatments of the epistemic uncertainties. These include safety factors, probabilistic approach disregarding redesign and regarding redesign, treating epistemic uncertainty and aleatory uncertainty the same, and more conservative treatment of the epistemic uncertainty. We demonstrate that the proposed approach can allow tradeoff of system performance against development cost (probability of redesign), while a standard reliability based design optimization, which does not take into account future redesign, provides only a single point on the tradeoff curve. We also show that the tradeoff can be achieved even with the traditional safety factor approach, without any probabilistic optimization. Furthermore, we investigate different treatments of epistemic error for probability of failure calculation. We find that it is possible to design to the 95th percentile of the probability of failure with modest mass penalty compared to treating epistemic and aleatory uncertainty alike.

The study on epistemic uncertainty due to the lack of knowledge has received increasing attention in risk assessment, reliability analysis, decision making, and design optimization. Different theories have been applied to model and quantify epistemic uncertainty. Research on sensitivity analysis for epistemic uncertainty has also been initialized. Sensitivity analysis can identify the contributions of individual input variables with epistemic uncertainty to the model output. It then helps guide the collection of more information to reduce the effect of epistemic uncertainty. In this paper, an effective sensitivity analysis method for epistemic uncertainty is proposed when both epistemic and aleatory uncertainties exist in model inputs. This method employs the unified uncertainty analysis framework to calculate the plausibility and belief measures. The gap between belief and plausibility measures is used as an indicator of the effect of epistemic uncertainty on the model output. The Kolmogorov-Smirnov distance between the two measures is used to quantify the main effect and the total effect of each independent variable with epistemic uncertainty. By the Kolmogorov-Smirnov distance, the importance of each variable is ranked. The feasibility and effectiveness of the proposed method is demonstrated with two engineering examples.

Key Points Methods are provided to quantify information and uncertainty in data Best achievable model performance for a given data set is estimated Model adequacy is characterized in terms of Aleatory and Epistemic Uncertainties

An approach to combining unreliable pieces of evidence and their propagation in a system response analysis

Pressure systems contain hazardous fluids within industrial processes. Inspection plays a vital role in managing the reliability of these safety-critical systems. It allows engineers to identify, characterize, and manage degradation of pressure vessels, piping, and associated equipment to prevent failure and the associated consequences on people and the environment. Mixed uncertainty can affect decision-making in at least three distinct aspects of inspection practice: inspection planning, inspection data analysis, and integrity assessment. Despite this, the inspection engineering discipline lacks methodologies for handling both aleatory and epistemic uncertainties within analyses, which could be expensively misleading. This paper demonstrates the benefits of applying mixed uncertainty quantification and analysis techniques to pressure vessel inspection and integrity assessment through a worked example, which shows how the epistemic and aleatory uncertainty in inspection data can be represented using an imprecise probability approach. The limitations of empirical data are shown to pose challenges to implementing these techniques in practice, and so practical requirements for a framework for implementing uncertainty analysis methods in inspection are proposed. These include, for example, the ability to generate meaningful yet conservative results from even a limited amount of poor-quality data, while allowing results to be bounded more narrowly as more data is collected, findings from better data are pooled, or engineering judgment and assumptions are applied.

Aiming at providing more accurate information for the first restoration, overhaul and maintenance of airborne products, this paper gives a calendar life assessment method for airborne products considering epistemic and aleatory uncertainty on the basis of investigation and analysis for the factors which affect the uncertainty of calendar life assessment. The uncertainty of calendar life is modeled as two types: epistemic uncertainty and aleatory uncertainty. a aleatory uncertainty model of calendar life based on interval analysis and blind number theory is given with parameter sensitivity analysis. Considering the designer's problem of incomplete cognition of failure mechanism, a measurement method of epistemic uncertainty is given based on the concept of confidence reliability.

Assessment of remaining service life of deteriorated concrete bridges under imprecise probabilistic information

One of the major challenges in probabilistic seismic hazard analysis (PSHA) studies, particularly for risk-based decision-making, is to constrain epistemic uncertainties. Epistemic uncertainty associated with ground-motion characterization (GMC) models exerts a strong influence on the hazard estimate for a given target level of ground shaking. In the Indian context (mainly along the Himalayan arc), constraining epistemic uncertainty is a significant challenge owing to the lack of recorded data. This study investigates the epistemic uncertainty associated with ground-motion models (GMMs) considered appropriate for the Himalayan region. First, a review of GMMs considered applicable to the Himalayan region is provided. Subsequently, a graphical comparison of median models is performed, followed by residual and statistical analysis. The evaluation utilizes observations from a recently compiled strong-motion dataset across the Himalayas and Indo-Gangetic plains of northern India. The dataset comprises 519 acceleration traces from 150 events in the moment magnitude (Mw) range Mw 3–7.4, recorded at epicentral distances in the range REpi<300 km. The analysis demonstrates significant between-model variability, particularly with regard to median magnitude and distance scaling. The residual analysis also indicates a large bias and aleatory uncertainty. Moreover, some of the GMMs exhibit trends with distance and magnitude. Overall, our evaluation analysis shows that there is clearly significant aleatory and epistemic uncertainty associated with the GMC modeling owing to the paucity of recorded data. The range of epistemic uncertainty represented by the GMMs (available in the literature) is much larger than that typically captured by the (multiple) global models often used in PSHA studies across India.

This is the second of two companion papers on improved intensity measures of strong seismic ground motions for use in probabilistic seismic demand analysis of reinforced concrete frame buildings. The first paper discusses the development of improved intensity measures. This paper describes the application of the developed intensity measures in probabilistic seismic demand analysis. The application is illustrated on the three reinforced concrete frame buildings (4, 10, and 16-storey high) that were used in the first paper. This involved computations of the seismic responses of the structures and the seismic hazard using the improved intensity measures. The response and the hazard results were then combined by means of probabilistic seismic demand analysis to determine the mean annual frequencies of exceeding specified response levels due to future earthquakes (i.e., the probabilistic seismic demands). For the purpose of comparison, probabilistic seismic demand analyses were also conducted by employing the spectral acceleration at the fundamental structural periods (Sa(T1)) as an intensity measure, which is currently the most used in practice. It was found that the use of the improved intensity measures results in significantly lower seismic demands relative to those corresponding to the intensity measure represented by Sa(T1), especially for long period structures.

Ship design optimization with mixed uncertainty based on evidence theory

This study applies the unit tsunami method and probabilistic tsunami hazard analysis to investigate the tsunami hazard for the southern region of Pingtung County in southern Taiwan. The FUNWAVE-TVD model is used to calculate the aleatory and epistemic uncertainties. The aleatory uncertainty is analyzed using a comparison of simulated and observed maximum tsunami wave heights and the epistemic uncertainty is evaluated using a scenario caused by earthquakes in the Manila and Ryukyu subduction zones according to probabilistic seismic hazard analysis in Taiwan using Senior Seismic Hazard Analysis Committee Level 3 methodology. A unit tsunami method database is established for the Manila and Ryukyu subduction zones and used to carry out a probability-based offshore tsunami wave height simulation for the southern region of Pingtung County. A hazard map for tsunamis caused by earthquakes in the Manila and Ryukyu subduction zones is also derived.

Uncertainty design can take account of aleatory and epistemic uncertainty in optimal processes. Aleatory uncertainty and epistemic uncertainty can be expressed as evidence theory uniformly, and evidence theory is used to describe the uncertainty. Transferring and response with evidence theory for structural optimal design are introduced. The principle of response evaluation is also set up. Finally, the cantilever beam in a test system is optimized in the introduced optimization process, and the results are estimated by the evaluation principle. The optimal process is validated after the optimization of beam.