Effect Of Epistemic Uncertainty Research Articles

Robustness assessment of RC structures designed for progressive collapse under multiple hazards

The goal of robustness assessment is to enable stakeholders to obtain efficient information, for reducing potential adverse effects of hazards before a natural disaster occurs, to obtain more realistic evaluation results and retrofit alternatives. A series of tests were carried out to investigate the effect of secondary beam on resisting progressive collapse. To further estimate the structural performance, a risk-based fuzzy conditional robustness assessment approach is established. The developed framework is applied to three various design RC structures subjected to multiple hazards, which is simulated by OpenSEEsPy. In this framework, the effect of the dependence configuration and the epistemic uncertainty on the vulnerability curves, loss-PGA curves, and the robustness index are studied by introducing the Vine-Copula and fuzzy theories. Results show that the effect of epistemic uncertainty on the hazard consequence becomes more pronounced with the increasing of PGA, and the lack of such consideration causes incurring additional retrofit costs for the stakeholders. Moreover, the fuzzy conditional robustness index of the models indicated that the installation of secondary beam showed a superior performance, compared with another reinforcement strategy of additional steel ratio. Finally, a method of survival probability-based robustness assessment is built on the developed assessment procedure and verified.

Belief reliability analysis of multi-state deteriorating systems under epistemic uncertainty

Due to the growing complexity of multi-state deteriorating systems and the lack of data, information and knowledge, epistemic uncertainty cannot be ignored anymore. Although there already exist some reliability metrics to deal with epistemic uncertainty problems in multi-state deteriorating systems, the final results provided by these methods are always probability intervals, which will suffer from the interval extension challenge in the subsequent operation. In this paper, we propose a reliability analysis method for the multi-state deteriorating system based on belief reliability theory, which can provide more conservative estimations and avoid interval extension problems. To describe the state transition process of multi-state deteriorating systems under the effect of epistemic uncertainty, a mathematical model called uncertain state transition chain is proposed. Under the framework of uncertainty theory, a total uncertainty inequality is given to assist the calculation of belief reliability. Using the proposed model and inequality, an algorithm of belief reliability for multi-state deteriorating systems considering the uncertainty of inspection time is provided. As a numerical example, the calculating process, the evaluation result and some discussions of a specific deteriorating system are given at last.

Risk-based assessment of breakwater armour units including effect of epistemic uncertainty on wave hazard

A formulation to assess a breakwater damage probability and to select the optimal maintenance strategy is presented and illustrated with a case study in Mexico. The formulation includes the calculation of annual and lifetime exceedance damage probabilities, the cost of damage/failure consequences, epistemic uncertainty and information on port logistics. The limit-state corresponds to the stability of the breakwater core (armour) units and the cost of failure consequences includes the explicit consideration of costs of fatalities, loss of armour units, damage and loss of property to port facilities, and economic loss due to business interruption in the port. The Van der Meer approach is followed to describe the damage state and the number of waves is modelled as lognormal instead of normal. A curve of tetrapod’s weight versus wave height is proposed as an approximation to the tetrapod’s fragility. FOSM (First Order Second Moments) and MCS (Monte Carlo simulation) techniques are implemented. The wave height is identified, through the calculation of gradients, as the most sensitive parameter for epistemic uncertainty. The optimal maintenance is selected after assessing three maintenance alternatives by balancing costs and safety. A breakwater located in Mexico called Tampico Port is used as case study to illustrate the formulation.

Evaluation of tropical cyclone recurrence rate: factors contributing to epistemic uncertainty

In this paper, we identify, assess and characterize epistemic uncertainties associated with the estimation of tropical cyclone storm recurrence rates. To illustrate the potential effects of epistemic uncertainty, we develop a range of storm surge recurrence rates at representative locations along the North Atlantic coast of the USA. We further illustrate how storm rate uncertainty impacts estimates of storm surge hazards. We consider the following factors when evaluating epistemic uncertainty in storm recurrence rate: (1) use of recorded storm track data versus interpolated storm track data, (2) the weighting method used for “counting” historical storms in the vicinity of the representative sites, (3) the kernel size used in the selected weighting method, (4) the intensity parameter used to filter “inconsequential storms” from the historical record, (5) the threshold value associated with the selected intensity filter, (6) the historical time period considered in the evaluation and (7) the impact of coastline geometry definition when partitioning storm populations. We observe that storm rate varies over orders of magnitude when considering these combinations of factors. When considering the effect of epistemic uncertainty in storm recurrence rate on estimated storm hazards, we find that the corresponding range of storm surge elevation spans multiple meters for a given annual exceedance frequency.

Interval-Valued Uncertainty Based on Entropy and Dempster-Shafer Theory

This paper presents a new structure as a simple method at two uncertainties (i.e., aleatory and epistemic) that result from variabilities inherent in nature and a lack of knowledge. Aleatory and epistemic uncertainties use the concept of the entropy and Dempster-Shafer (D-S) theory, respectively. Accordingly, we propose the generalized Shannon entropy in the D-S theory as a measure of uncertainty. This theory has been originated in the work of Dempster on the use of probabilities with upper and lower bounds. We describe the framework of our approach to assess upper and lower uncertainty bounds for each state of a system. In this process, the uncertainty bound is calculated with the generalized Shannon entropy in the D-S theory in different states of these systems. The probabilities of each state are interval values. In the current study, the effect of epistemic uncertainty is considered between events with respect to the non-probabilistic method (e.g., D-S theory) and the aleatory uncertainty is evaluated by using an entropy index over probability distributions through interval-valued bounds. Therefore, identification of total uncertainties shows the efficiency of uncertainty quantification.

Belief Reliability for Uncertain Random Systems

Measuring system reliability by a reasonable metric is a common problem in reliability engineering. Since real systems are usually uncertain random systems affected by both aleatory and epistemic uncertainties, existing reliability metrics are unreliable. This paper proposes a general reliability metric, called belief reliability metric, to cope with the problem. In this paper, the belief reliability is defined as the chance that a system state is within a feasible domain. Mathematically, the metric can degenerate to either probability theory-based reliability, which copes with aleatory uncertainty, or uncertainty theory-based reliability, which considers the effect of epistemic uncertainty. Based on the proposed metric, some commonly used belief reliability indexes, such as belief reliability distribution, mean time to failure, and belief reliable life, are introduced. We also develop system belief reliability formulas for different systems configurations. To further illustrate the formulas, a real case study is performed.

Hybrid spatial uncertainty analysis for the estimation of imprecise failure probabilities in Laser Sintered PA-12 parts

This paper presents the application of non-deterministic modelling techniques for the quantification of imprecise failure probabilities in PA-12 parts produced via Laser Sintering (LS). Specifically, a modelling approach consisting of a combination of interval and random fields is applied, and the effect hereof on the resulting polymorphic uncertainty in the mechanical performance of the LS parts is studied. A link with the underlying process physics is given, relating the spatial porosity distributions that are inherently present in LS PA12 parts to a spatial distribution in the apparent Young’s modulus. Furthermore, uncertainty on the final dimensions of other parts that are constructed in the same build envelope as the designed part is linked to uncertainty in the cross-sectional area of the designed part.The effect of these sources of uncertainty is studied in three case studies, illustrating the need for a well-thought production process planning given the influence on the resulting mechanical performance of the designed structure. Especially the effect of epistemic uncertainty on the design process is shown to be significant.

Effects of Epistemic Uncertainty in Seismic Hazard Estimates on Building Portfolio Losses

In catastrophe risk modeling, a defensible estimation of impact severity and its likelihood of occurrence to a portfolio of assets can only be made through a rigorous treatment of uncertainty and the consideration of multiple alternative models. This approach, however, requires repeating lengthy calculations multiple times. To limit the demand on computational time and resources, a frequent practice in the industry is to estimate the distribution of earthquake-induced portfolio losses using a simulated catalog of events from a single representative mean ground motion hazard model for the region. This simplified approach is faster but may provide biased estimates of the likelihood of occurrence of the large and infrequent losses that drive many risk mitigation decisions. Investigation through case studies of different portfolios of assets located in the San Francisco Bay Region shows the potential for both a bias in the mean loss estimates and an underestimation of their central 70% interpercentile. We propose a simplified and computationally practical approach that reduces the bias in the mean portfolio loss estimates. This approach does not improve the estimate of the inter-percentile range, however, a quantity of no direct practical use.

Benchmarking nutrient use efficiency of dairy farms: The effect of epistemic uncertainty

The nutrient use efficiency (NUE) of a system, generally computed as the amount of nutrients in valuable outputs over the amount of nutrients in all inputs, is commonly used to benchmark the environmental performance of dairy farms. Benchmarking the NUE of farms, however, may lead to biased conclusions because of differences in major decisive characteristics between farms, such as soil type and production intensity, and because of epistemic uncertainty of input parameters caused by errors in measurement devices or observations. This study aimed to benchmark the nitrogen use efficiency (NUEN; calculated as N output per unit of N input) of farm clusters with similar characteristics while including epistemic uncertainty, using Monte Carlo simulation. Subsequently, the uncertainty of the parameters explaining most of the output variance was reduced to examine if this would improve benchmarking results. Farms in cluster 1 (n=15) were located on sandy soils and farms in cluster 2 (n=17) on loamy soils. Cluster 1 farms were more intensive in terms of milk production per hectare and per cow, had less grazing hours, and fed more concentrates compared to farms in cluster 2. The mean NUEN of farm in cluster 1 was 43%, while in cluster 2 it was 26%. Input parameters that explained most of the output variance differed between clusters. For cluster 1, input of feed and output of roughage were most important, whereas for cluster 2, the input of mineral fertilizer (or fixation) was most important. For both clusters, the output of milk was relatively important. Including the epistemic uncertainty of input parameters showed that only 37% of the farms in cluster 1 (out of 105 mutual comparisons) differed significantly in terms of their NUEN, whereas in cluster 2 this was 82% (out of 120 comparisons). Therefore, benchmarking NUEN of farms in cluster 1 was no longer possible, whereas farms in cluster 2 could still be ranked when uncertainty was included. After reducing the uncertainties of the most important parameters, 72% of the farms in cluster 1 differed significantly in terms of their NUEN, and in cluster 2 this was 87%. Results indicate that reducing epistemic uncertainty of input parameters can significantly improve benchmarking results. The method presented in this study, therefore, can be used to draw more reliable conclusions regarding benchmarking the NUE of farms, and to identify the parameters that require more precision to do so.

Estimating burnup uncertainties in KSU TRIGA Mark II reactor and their impact on reactor safety

Safety analysis was conducted for the KSU TRIGA Mark-II reactor to assess the safety impact of loading enriched fuel in the reactor core. This analysis was performed using a representative single channel conservative model in the best estimate thermal-hydraulic code RELAP5/MOD3.3. However the effects of epistemic uncertainties on the safety calculations and sensitivity of the model towards these uncertainties can play a critical role in decision-making. One of the major uncertainties in the input parameters for RELAP model can be in the axial power peaking factors attributed to uncertainties in burnup estimates. The uncertainty propagation through different models and sensitivity analysis were studied with the help of established tools such as MCNP and RELAP5/MOD3.3. The results of these sensitivity studies due to uncertainties in the burnup values were compared with the sensitivity to uncertainties within the thermal-hydraulic model.

A concurrent reliability optimization procedure in the earlier design phases of complex engineering systems under epistemic uncertainties

Concurrent engineering has obtained increasing attention to solve the design problems of multidisciplinary systems. In practical engineering, there are epistemic uncertainties during whole design cycle of complex systems. Especially in earlier design phases, the effects of epistemic uncertainties are not usually easy to be quantified. It is because design information is insufficient. Furthermore, commonly used probability theory is also not suitable to be utilized. In this situation, epistemic uncertainties will be introduced unavoidably by mathematical models or simulation tools and may affect the performance of complex system significantly. To solve this problem, evidence theory is introduced and combined with the collaborative optimization method in this study. An evidence-based collaborative reliability optimization method is also proposed. Evidence theory is a powerful approach to handle epistemic uncertainties by Plausibility and Belief. Meanwhile, collaborative optimization is widely utilized in the concurrent design of complex systems. An aircraft conceptual design problem is utilized to show the application of the proposed method.

Stochastic Multidisciplinary Analysis Under Epistemic Uncertainty

This paper presents a probabilistic framework to include the effects of both aleatory and epistemic uncertainty sources in coupled multidisciplinary analysis (MDA). A likelihood-based decoupling approach has been previously developed for probabilistic analysis of multidisciplinary systems, but only with aleatory uncertainty in the inputs. This paper extends this approach to incorporate the effects of epistemic uncertainty arising from data uncertainty and model errors. Data uncertainty regarding input variables (due to sparse and interval data) is included through parametric or nonparametric distributions using the principle of likelihood. Model error is included in MDA through an auxiliary variable approach based on the probability integral transform. In the presence of natural variability, data uncertainty, and model uncertainty, the proposed methodology is employed to estimate the probability density functions (PDFs) of coupling variables as well as the subsystem and system level outputs that satisfy interdisciplinary compatibility. Global sensitivity analysis (GSA), which has previously considered only aleatory inputs and feedforward or monolithic problems, is extended in this paper to quantify the contribution of model uncertainty in feedback-coupled MDA by exploiting the auxiliary variable approach. The proposed methodology is demonstrated using a mathematical MDA problem and an electronic packaging application example featuring coupled thermal and electrical subsystem analyses. The results indicate that the proposed methodology can effectively quantify the uncertainty in MDA while maintaining computational efficiency.

구조물의 최적안전지수와 생애주기비용의 상관관계에 관한 연구

본 연구는 구조물의 최적안전수준과 수명기간동안 투자되는 총비용과의 상관관계를 연구하였다. 설계, 건설 및 공용 중 투자되는 총비용을 최소화하면서 최적의 안전수준을 결정하기 위하여 신뢰성해석을 수행하였다. 신뢰성해석에는 설계인자들의 불확실성과 설계 및 공사, 유지관리를 수행하는 인간의 오류 등 인적 불확실성을 확률변수로 고려하였다. 이러한 확률해석을 통한 안전지수와 생애주기비용의 상관관계를 연구하고, 생애주기비용의 분산도에 따른 안전지수의 민감도해석을 통하여 최적의 안전수준을 결정하였다. 해석결과는 이러한 평가방법이 교통시설물에 투자되는 비용을 최소화하면서 최적의 안전수준을 결정할 수 있는 정확하고 유용한 방법임을 보여주었다. This study was intend to develop the optimal design method of suspension bridge by the reliability analysis based on minimization of life cycle cost(LCC). The reliability analysis was performed considering aleatory uncertainties included in the result of numerical analysis. The optimal design was estimated based on life-cycle cost analysis depending on the result of reliability analysis. As the effect of epistemic uncertainty, the safety index (beta), failure probability (pf) and minimum life cycle cost were random variables. The high-level distributions were generated, from which the critical percentile values were obtained for a conservative bridge design through sensitivity assessment.

Optimal Design of Suspension Bridge Based on Minimization of Life Cycle Cost

This study was intend to develop the optimal design method of suspension bridge by the reliability analysis based on minimization of life cycle cost (LCC). The reliability analysis was performed considering aleatory uncertainties included in the result of numerical analysis. The optimal design was estimated based on life-cycle cost analysis depending on the result of reliability analysis. As the effect of epistemic uncertainty, the safety index (beta), failure probability (pf) and minimum life cycle cost were random variables. The high-level distributions were generated, from which the critical percentile values were obtained for a conservative bridge design through sensitivity assessment.

Corrosion initiation time updating by epistemic uncertainty as an alternative to schedule the first inspection time of pre-stressed concrete vehicular bridge beams

As traffic demands grow constantly and some vehicle bridges deteriorate because of corrosion issues, bridge agencies require non-expensive procedures to support decisions about cost-effective maintenance schedules. In this article, a reliability-based formulation is proposed for the prediction of the optimal first inspection time including both the corrosion deterioration and the epistemic uncertainty on the corrosion initiation time. For the identification of the bridge integrity state, where little or no follow-up has been previously developed, the prediction of a damage state implies a great deal of epistemic uncertainty. The impact of this kind of uncertainty on the corrosion initiation time prediction is appraised in order to include the conservative estimations of such a time, according to the bridge revenues/cost ratio of further and more detailed studies. The time-varying bridge reliability is calculated in terms of the bridge corrosion deterioration, which induces a moment capacity reduction of the bridge beams. Epistemic uncertainty is introduced in the corrosion initiation time, and the optimal first inspection time is obtained as a probability distribution. Consequently, a procedure to calculate the first time for inspection on girder bridges has been proposed, based on updating a known distribution after considering the effect of epistemic uncertainty, using a lognormal distributed factor as ‘evidence’, by means of the Markov chain Monte Carlo technique.

An application of the Kriging method in global sensitivity analysis with parameter uncertainty

For structural systems with both epistemic and aleatory uncertainties, the effect of epistemic uncertainty on failure probability is measured by the variance based sensitivity analysis, which generally needs a “triple-loop” crude sampling procedure to solve and is time consuming. Thus, the Kriging method is employed to avoid the complex sampling procedure and improve the computational efficiency. By utilizing the Kriging predictor model, the conditional expectation of failure probability on the given epistemic uncertainty can be calculated efficiently. Compared with the Sobol’s method, the proposed one can ensure reasonable accuracy of results but with lower computational cost. Three examples are employed to demonstrate the reasonability and efficiency of the proposed method.

Uncertainty Analysis of Air Radiation for Lunar-Return Shock Layers

Uncertainty Analysis of Air Radiation for Lunar-Return Shock Layers

Simplified method for seismic risk assessment of buildings with consideration of aleatory and epistemic uncertainty

A simplified method for seismic risk assessment with consideration of aleatory and epistemic uncertainties is proposed based on the widely used closed-form solution for estimating the mean annual frequency of exceeding a limit state (LS). The method for the determination of fragility parameters involves a non-linear static analysis of a set of structural models, which is defined by utilising Latin hypercube sampling, and non-linear dynamic analyses of equivalent single degree-of-freedom models. The set of structural models captures the epistemic uncertainties, whereas the aleatory uncertainty due to the random nature of the ground motion is, as usual, simulated by a set of ground motion records. Although the method is very simple to implement, it goes beyond the widely used assumption of independent effects due to aleatory and epistemic uncertainty. Thus, epistemic uncertainty has a potential influence on both fragility parameters, and not only on dispersion, as has been assumed in some other approximate methods. The proposed method is applied to an example of a four-storey reinforced concrete building, where it is shown that the effects of epistemic uncertainties, in addition to aleatory uncertainty, increase with the severity of the LS, so that, for the near collapse LS, the risk with consideration of both sources of uncertainty is more than double if compared to the risk, which was determined solely by the consideration of aleatory uncertainty.

Design Under Uncertainty: Balancing Expected Performance and Risk

The problem of quantifying uncertainty in the design process is approached indirectly. Nonquantifiable variability resulting from lack of knowledge is treated as epistemic uncertainty and quantifiable variability caused by random influences is treated as aleatory uncertainty. The emphasis in this approach is on the effects of epistemic uncertainty, left unquantified, on design performance. Performance is treated as a random function of the epistemic uncertainties that are considered as independent variables, and a design decision is based on the mean and variance of design performance. Since the mean and variance are functions of the uncertainties, multicriteria decision methods are employed to determine the preferred design. The methodology is illustrated on a three-spring model with stochastic forcing and two uncertain damping coefficients. Based on the example, the concept of balancing expected performance and risk is explored in an engineering context. Risk is quantified using aleatory uncertainty for fixed values of epistemic uncertainty. The study shows the unique features of this approach in which risk-based design decisions are made under both aleatory and epistemic uncertainties without assuming a distribution for epistemic uncertainty.