Traditional Uncertainty Analysis Research Articles

Non-probabilistic credible reliability analysis of the composite laminate

For the reliability analysis of composite laminate structures, there is a problem of difficult data acquisition. Traditional reliability analysis methods require a large amount of data to maintain calculation accuracy. Therefore, the traditional reliability analysis method is not applicable to composite laminates. For the above-mentioned problems, this paper presents a method to calculate the credible reliability of composite laminate structures using the Bayesian theorem. The method is distinguished from the traditional uncertainty analysis methods. The likelihood function and the newly introduced samples are first used to correct the prior distribution of the uncertain parameters. Furthermore, the posterior distribution, containing information from both the sample and prior distributions, can be obtained. Ultimately, based on the acquired posterior distribution, the probability density function can be updated with newly introduced samples. Using the Hashin failure criterion, the failure probabilities of the fibers and matrix of the composite laminate structure are quantified, respectively. Then, the credible reliability of the composite laminate is obtained. Numerical example results show the proposed method can maintain high accuracy with fewer samples and demonstrate the validity of the model. For the numerical calculations, the deterministic parameters of the distribution function and the functional distribution parameters were verified, composite laminates and aircraft wing structures were analyzed. The experimental results show that the error between the probability density function of the parameters and the probability density function predicted by the sample is less than 0.045. Compared with the traditional reliability analysis methods for composite structures, this method can effectively measure the credible reliability of composite laminate structures with fewer samples and similar accuracy. The method enables real-time updating of the parameter probability density function by newly introduced samples and improves the confidence level.

Bayesian model evaluation for multiple scenarios

Traditional uncertainty analysis for subsurface models is typically based on a single dynamic model with a number of uncertain parameters. Improved and more robust forecasting can be obtained by combining several models in a Bayesian setting using model averaging. The traditional Bayesian Model Averaging (BMA), however, suffers from several drawbacks, such as too large sensitivity to prior model assumptions and instability with respect to measurement perturbations, especially when the number of measurements is large. We suggest a modified version of BMA (MBMA) where the calculations are stabilized using an ensemble of measurements. Bayesian stacking (BS) is a method that is directly focused on the performance of the combined predictive distribution of several models. The original version of BS (BSLOO) is based on leave-one-out cross-validation and requires a Bayesian inversion for each data point which may be very time consuming. We suggest a modified version of stacking (MBS) that requires only a single history match and uses an ensemble of measurements. MBS may be used with either prior (MBS-pri) or posterior (MBS-post) predictive distributions. The behavior of the methods is illustrated using three synthetic, linear examples. One is a simple mixture model. The other two are inspired by 4D seismic data. The results with MBS-pri are very similar to the results with MBMA. The results with MBS-post are similar to those of BSLOO when the data are uncorrelated. MBS can take into account correlated data or measurement errors, while correlations are neglected in the BSLOO weight calculations.

A Fast Method for Uncertainty Analysis of Power System Dynamic Simulation

Uncertain variables, such as electric power system parameters, have significant impacts on dynamic simulations of power systems. As traditional uncertainty analysis methods for power system dynamic simulations, both the simulation method and the approximation methods are difficult to balance the model complexity, computational efficiency, and simulation accuracy. In order to balance the model complexity, computational efficiency, and simulation accuracy, this paper proposes a method for uncertainty analysis for power system dynamic simulation based on the Nataf transformation and Gaussian-Hermite quadrature. Firstly, the samples on the normal distribution space are determined according to the Gaussian-Hermite quadrature points and the Nataf transformation. Secondly, obtain the simulation samples by inverse Nataf transformation, and perform power system dynamic simulation. Thirdly, the random output is approximated as a linear combination of a single random input, and the mean and standard deviation of the random output under the impact of a single random input are calculated by Gaussian-Hermite quadrature. Then, calculate the mean and standard deviation of the random output under the impact of all random input. Finally, the effectiveness of the proposed method is validated on the IEEE 9-bus system and IEEE 39-bus system. Compared with Monte Carlo simulation and Latin Hypercube sampling, the proposed method can greatly reduce the simulation time for uncertain dynamic simulations while maintaining high accuracy.

Reduced Space Optimization‐Based Evidence Theory Method for Response Analysis of Space‐Coiled Acoustic Metamaterials with Epistemic Uncertainty

Acoustic metamaterials have been widely concerned by researchers because of their excellent sound absorption properties. Traditional uncertainty analysis methods for response analysis of acoustic metamaterials with evidence variables have limitations. The excessive time spent on repetitive extreme analysis of focal elements severely impedes the practical application of evidence theory. To reduce the computational costs of uncertainty quantification for acoustic metamaterials under the evidence theory, a reduced space optimization‐based evidence theory method (RSO‐ETM) is proposed. In RSO‐ETM, a simplified surrogate model is first constructed by a modified adaptive arbitrary orthogonal polynomial (MAAOP) expansion method, and then, the monotonicity of the response surface is examined to reduce the space. Subsequently, the Newton iteration technique and a transformation boundary method are used to obtain the extreme points in the reduced space, through which the boundary of the response over each focal element can be readily obtained. By using RSO‐ETM, the optimization for each focal element can be avoided, and correspondingly the computational costs are reduced. Two mathematical examples and acoustic problems are employed to demonstrate the practicality of the methods.

Polynomial chaos expansion based sensitivity analysis of predicted knee reactions—assessing the influence of the primary ligaments in distraction based models

Computational knee models have shown that predicted condylar reactions are sensitive to the utilized ligament mechanical parameters. These models, however, are computationally expensive with multiple sources of uncertainty. Traditional uncertainty analysis using Monte-Carlo (MC) inspired methods are costly to perform. The purpose of this study was to use two example calibrated knee models to compare quasi-MC versus polynomial chaos expansion (PCE) sensitivity analyses of predicted condylar reactions that included uncertainty in the mechanical parameters of the ligaments. PCE was practically identical versus quasi-MC with 95% and 98% reductions in model evaluations for analyses with 10 and 6 uncertain variables, respectively.

A modified isotope-based method for potential high-frequency evapotranspiration partitioning

To better understand water and energy cycles, numerous efforts to partition evapotranspiration (ET) into evaporation (E) and transpiration (T) have been made over the recent half century. One of the analytical methods is the isotopic approach. The isotopic composition of ET (δET) is a crucial parameter in the traditional isotope-based ET partitioning model, which however, has considerable uncertainty and high sensitivity. Here we proposed a modified T fraction in total ET (FT) calculation using Keeling plot slope (k), the atmospheric vapor concentration (Cv), and the isotopic composition of atmospheric vapor (δv), to avoid the direct use of δET. Following the traditional method, we used the Craig-Gordon model for the isotopic composition of evaporation (δE) and chamber method for the isotopic composition of transpiration (δT) in our modified method. The modified FT calculation method (FT (m)) can be applied at a 15-min time scale using the average values (FTi (mp)) and at a 1 Hz time scale for high-frequency method (FTi). The modified method was verified by both theoretical derivations and field observations. FTi (mp) was equivalent to those using the traditional isotopic method at a 15-min time scale. However, FTi eliminated the highly sensitive parameter δET, and redistributed the sensitivity of δET into three less sensitive parameters. Additionally, FTi has two main advantages. First, the high-frequency method avoids the extrapolation of the Keeling plot regression line intercept. Second, the high-frequency method can produce a 95% confidence interval of FT in a measurement cycle (e.g., 15 min). The calculated confidence interval was different from that of traditional uncertainty analysis. The high-frequency method might be useful when investigating evapotranspiration partitioning under short-term extreme weather events and flush agricultural irrigation.

The realities of managing uncertainties surrounding pluvial urban flood risk: An ex post analysis in three European cities

Inner‐city pluvial flooding is characterised by major uncertainties, often making response problematic. We explore this in London, Lisbon, and Rotterdam, through ex post document analysis and semi‐structured interviews. Traditional uncertainty analysis generally focuses on quantifiable factors, needing to clarify uncertainty for engineering design, flood warnings and incident management. But other uncertainties concern budgets, skills, legal issues, and politics. There are also many relevant certainties or near‐certainties, which can dominate. They need equal attention in understanding decision making for risk reduction. Responses to our cities' flood risks—including portfolios of engineering and non‐structural measures—also contain significant no‐regret components requiring less certainty about risk. Our cities appear to be positioned along a learning continuum, related to flood experience and the consequential uncertainty reduction. However progress can be worryingly slow. Only experiencing actual flood events promotes accelerated action and often the certainties concerning resource constraints also outweigh the many uncertainties in risk assessment.

A novel uncertainty analysis method for composite structures with mixed uncertainties including random and interval variables

This paper is aimed at proposing a novel uncertainty analysis approach based on polynomial chaos expansion method for composite structures, where mixed uncertainties including normal random and interval variables can be considered simultaneously. Firstly, existing uncertain elastic parameters in composites can be separately dealt with as normal random and interval variables according to the amount of available information and the uncertain response analysis problem with mixed uncertainties is proposed. Then some traditional uncertainty analysis methods are introduced, whose purpose is to point out the shortcomings or deficiencies for given approaches. Furthermore, the basic knowledge for polynomial chaos expansion (PCE) method and a novel uncertainty analysis method on the basis of PCE method for composite structures with mixed uncertainties are explained in details, where the polynomial coefficients are viewed as quadratic polynomial functions of interval variables. Finally, two numerical examples are carried out to account for the validity and feasibility of the developed method. The results show that the developed PCE method can be efficiently applied in uncertainty analysis of composite structures.

Dynamic Uncertainty Analysis for Random Vibration Signals in Flight Test

Random vibration signals with insufficient information can be obtained in flight tests. Traditional uncertainty analysis methods based on statistical theory cannot be employed when the precise probability density and trends are unknown. In this paper, a bootstrap gray method based on gray system theory and bootstrap method is proposed to dynamically analyze random vibration signals. A set of dynamic analysis indices, such as estimated value, variation domain, dynamic uncertainty, reliability, and mean uncertainty, are used to assess the effectiveness of the bootstrap gray method. A group of parameters is discussed to optimize the performance of the proposed method. For time series of random vibration signals, the analysis of variation domain demonstrates the superiority of the bootstrap gray method over the bootstrap method. The instantaneous fluctuation of time-varying signals can be accurately evaluated by dynamic uncertainty, for which prior information on the probability distribution is not taken into account. The statistical characteristic of dynamic uncertainty is quantified with mean uncertainty. The results show that the bootstrap gray method has an advantage in analyzing uncertainty for random vibration signals with insufficient information, and the reliability reaches 100% at the given confidence level.

Improving uncertainty estimation in urban hydrological modeling by statistically describing bias

Abstract. Hydrodynamic models are useful tools for urban water management. Unfortunately, it is still challenging to obtain accurate results and plausible uncertainty estimates when using these models. In particular, with the currently applied statistical techniques, flow predictions are usually overconfident and biased. In this study, we present a flexible and relatively efficient methodology (i) to obtain more reliable hydrological simulations in terms of coverage of validation data by the uncertainty bands and (ii) to separate prediction uncertainty into its components. Our approach acknowledges that urban drainage predictions are biased. This is mostly due to input errors and structural deficits of the model. We address this issue by describing model bias in a Bayesian framework. The bias becomes an autoregressive term additional to white measurement noise, the only error type accounted for in traditional uncertainty analysis. To allow for bigger discrepancies during wet weather, we make the variance of bias dependent on the input (rainfall) or/and output (runoff) of the system. Specifically, we present a structured approach to select, among five variants, the optimal bias description for a given urban or natural case study. We tested the methodology in a small monitored stormwater system described with a parsimonious model. Our results clearly show that flow simulations are much more reliable when bias is accounted for than when it is neglected. Furthermore, our probabilistic predictions can discriminate between three uncertainty contributions: parametric uncertainty, bias, and measurement errors. In our case study, the best performing bias description is the output-dependent bias using a log-sinh transformation of data and model results. The limitations of the framework presented are some ambiguity due to the subjective choice of priors for bias parameters and its inability to address the causes of model discrepancies. Further research should focus on quantifying and reducing the causes of bias by improving the model structure and propagating input uncertainty.

Evaluation of Aeroelastic Uncertainty Analysis Methods

DOI: 10.2514/1.47118 Flutter is a destructive and potentially explosive phenomenon that is the result of the simultaneous interaction of aerodynamic, elastic, and inertial forces. The nature of flutter mandates that flutter flight testing be cautious and conservative. Because of this, further investigation of uncertainty analysis with respect to the flutter problem is desiredandwarranted.Predictionof flutterinthetransonicregimerequirescomputationallyexpensivehigh-fidelity simulation models. Because of the computational demands, traditional uncertainty analysis is not often applied to transonic flutter prediction, resulting in reduced confidence in the results. The work described herein is aimed at exploring various methods to reduce the existing computational time limitations of traditional uncertainty analysis. Specifically,thecouplingofdesignofexperimentandresponsesurfacemethodsandtheapplicationofanalysisare appliedtoavalidatedaeroelasticmodeloftheAGARD445.6wing.Fromahigh-fidelitynonlinearaeroelasticmodel, a linear reduced-order model is produced that captures the essential dynamic characteristics. Using reduced-order models, the design of experiment, response surface methods, and -analysis approaches are compared with traditional Monte Carlo-based stochastic simulation. All of these approaches to uncertainty analysis have advantages and drawbacks. Results from these methods and their robustness are compared and evaluated. HE potentially explosive nature of flutter mandates that flutter flight testing be cautious and conservative. The development of a flutterstabilityparameterwasundertakenfourdecadesagotogivea more reliable technique to predict the onset of flutter. Other methods of predicting flutter such as damping versus velocity are known to have a number of shortcomings, one of which can be the sudden degradationindampingasillustratedintheexplosive flutterexample shown in Zimmerman and Weissenburger [1]. In this classic paper, the flutter stability parameter was developed using the classical two-dimensional, two-degree-of-freedom (pitch/plunge) aeroelastic wing model, and the technique was shown to be applicable for higher-degree-of-freedom analysis. The flutter stability parameter (flutter margin) is calculated using the decay rate and damped frequency. Traditionally, computational aeroelasticity for loads and flutter prediction combines a linear finite element formulation for the structure with linear aerodynamic methods. At the same time, the prediction of aerodynamic performance and control surface effectivenessaccountsfortheeffectsofthestructuralelasticdeformations on the external aerodynamics by means of correction factors applied to results obtained when the aircraft is assumed to be rigid. Both practices are well-established in aircraft design and give accurate, reliable, and rather inexpensive predictions for static and dynamic

A full Bayesian approach to generalized maximum likelihood estimation of generalized extreme value distribution

This study develops a full Bayesian GEV distribution estimation method (BAYBETA), which contains a semi-Bayesian framework of generalized maximum likelihood estimator (GMLE), to make full use of several advantages of the Bayesian approach especially in uncertainty analysis. For the full Bayesian framework, the optimal hyperparameter of beta prior distribution on the shape parameter of the GEV distribution is found as (6.4990, 8.7927) through simulation-based analysis. In a performance comparison analysis, the performances of BAYBETA, which adopts beta(6.4990, 8.7927) as prior density on the shape parameter of the GEV distribution, are almost the same as or slightly better than GML, outperforming MOM, ML, and LM in terms of root mean square error (RMSE) and bias when the shape parameter is negative. Also, a case study of two hydrologic extreme value data shows that the traditional uncertainty analysis using asymptotic approximation of ML and GML has limitations in describing the uncertainty in high upper quantiles, while the proposed full Bayesian estimation method BAYBETA provides a consistent and complete description of the uncertainty.

Partitioning Spatial Model Uncertainty Based on Joint Spatial Simulation

AbstractIn this study, an uncertainty analysis procedure for joint sequential simulation of multiple attributes of spatially explicit models used in geographical informational systems was developed based on regression analysis. This procedure utilizes information obtained from joint sequential simulation to establish the relationship between model uncertainty and variation of model inputs. Using this procedure, model variance can be partitioned by model input parameters on a cell by cell basis. In the partitioning, the correlation of neighboring cells is accounted for. With traditional uncertainty analysis methods, this is not possible. In a case study, spatial variation of soil erodibility from a joint sequential simulation of soil properties was analyzed. The results showed that the regression approach is a very effective method in the analysis of the relationship between variation of the model output and model input parameters. It was also shown for the case study that: (1) the uncertainty of soil erodibility of a cell is mainly propagated from its own soil properties; (2) the interactions of soil properties of neighboring cells could reduce uncertainty of soil erodibility; (3) it is sufficient for uncertainty analysis to include the nearest three neighboring cell groups; and (4) the largest uncertainty contributors vary by soil properties and location.

AN UNCERTAINTY ANALYSIS PROCEDURE FOR SPATIALLY JOINT SIMULATIONS OF MULTIPLE ATTRIBUTES

In this study, an uncertainty analysis procedure for joint sequential simulation of multiple attributes of spatially explicit models was developed based on regression analysis. This procedure utilizes information obtained from joint sequential simulation to establish the relationship between model uncertainty and variation of model inputs. Using this procedure, model variance can be partitioned by model input parameters on a pixel by pixel basis. In the partitioning, the correlation of neighboring pixels is accounted for. With traditional uncertainty analysis methods, this is not possible. In a case study, spatial variation of soil erodibility from a joint sequential simulation of soil properties was analyzed. The results showed that the regression approach is a very effective method in the analysis of the relationship between variation of the model and model input parameters. It was also shown for the case study that (1) uncertainty of soil erodibility of a pixel is mainly propagated from its own soil properties, (2) soil properties of neighboring pixels contribute negative uncertainty to soil erodibility, (3) it is sufficient for uncertainty analysis to include the nearest three neighboring pixel groups, and (4) the largest uncertainty contributors vary by soil properties and location.