Influence Of Input Uncertainty Research Articles

Learnable quantile polynomial chaos expansion: An uncertainty quantification method for interval reliability analysis

Various uncertainties like random input and data noise in aerospace engineering affect flight vehicle safety, making uncertainty quantification important for improving system reliability. Polynomial chaos expansion (PCE) is a versatile method for quantifying stochastic systems’ uncertainty caused by random input, while it cannot quantify data uncertainty caused by noise. To solve this problem, a novel uncertainty quantification method, learnable quantile PCE (LQPCE), is proposed for interval reliability analysis. Unlike the traditional PCE, the multi-dimensional orthonormal basis is constructed for combination input rather than only random variables, and the expansion coefficients are parameterized to learnable weights, ensuring the LQPCE model can capture data noise’s features. The LQPCE Pinball loss function is constructed to learn parameterized expansion coefficients by quantile level iterative sampling, achieving accurate prediction and data uncertainty quantification. The quantified data uncertainty is used for interval reliability analysis, calculating more reliable results about the influence of input uncertainty on stochastic systems’ reliability. Three numerical examples and one engineering application validate the LQPCE method’s effectiveness. The results show that the LQPCE method can quantify data uncertainty accurately and obtain credible interval reliability.

Stochastic natural frequency analysis of varying diameter functionally graded material pipe conveying fluid

This paper investigates the uncertainty of the structure and material parameters on the natural frequency of the varying diameter functionally graded material (FGM) pipe conveying fluid. Firstly, concentrating on the spatially dependent uncertainty of geometry varying in axial direction as well as the material varying in radial direction, the random field is employed to describe the uncertainty parameters. Then, a generalized eigenvalue equation of the varying diameter FGM pipe is derived by the dynamic stiffness method while introducing the random field and variables into the deterministic governing equation. Due to the input uncertainty, the natural frequencies of the varying diameter FGM pipe change to random variables. In this respect, the stochastic characteristics of natural frequencies can be approximated by the Monte Carlo simulation. However, the enormous computational cost is unbearable. The efficient artificial neural network surrogate model is introduced and incorporated for the natural frequency uncertainty quantification. Consequently, a stochastic natural frequency analysis approach based on the neural network is proposed for the varying diameter FGM pipe conveying fluid. Some examples are investigated to illustrate the effectiveness of the proposed method and the influence of input uncertainty on the probabilistic characterization of the natural frequencies.

UNCERTAINTY PROPAGATION FOR LWR BURNUP BENCHMARK USING SAMPLING BASED CODE SCALE/SAMPLER

Sampling based method is adopted in many fields of engineering and it is currently used to propagate uncertainties from physical parameters and from nuclear data, to integral indicators of nuclear systems. The total uncertainty associated with a model simulation is of major importance for safety analysis and to guide vendors about acceptable tolerance limits for nuclear installations parts. This work presents some calculations to propagate uncertainties for a nuclear reactor fuel element modeled in SCALE/TRITON, using the sampling tool SCALE/SAMPLER. Results showed that that the influence of input uncertainties on kinf is more pronounced in the fresh core other than the depleted core and the contribution from studied manufacturing uncertainties is smaller than the contribution of nuclear data uncertainties.

A new kind of sensitivity index for multivariate output

Mathematical and computational models with correlated multivariate output are commonly used for risk assessment and decision support in engineering. Traditional methods for sensitivity analysis of the model with scalar output fail to provide satisfactory results for this multivariate case. In this work, we introduce a new sensitivity index which looks at the influence of input uncertainty on the entire distribution of the multivariate output without reference to a specific moment of the output. The definition of the new index is based on the multivariate probability integral transformation (PIT), which can take into account both of the uncertainties and the correlations among multivariate output. The mathematical properties of the proposed sensitivity index are discussed and its differences with the sensitivity indices previously introduced in the literature are highlighted. Two numerical examples and a rotating shaft model of an aircraft wing are employed to illustrate the validity and potential benefits of the new sensitivity index.

Simulating the fate and transport of nursery-box-applied pesticide in rice paddy fields.

The Pesticide Concentration in a Paddy Field model (PCPF-1) was modified by adding a root zone compartment to simulate nursery-box-applied (NB-applied) pesticide. The PCPF-NB model was validated for predicting the concentrations of NB-applied fipronil and imidacloprid in rice paddy fields using two treatment methods: before transplanting (BT) and at sowing (AS). Uncertainty and sensitivity analyses were used to evaluate the robustness of the concentrations predicted by the model. The hourly predicted concentrations of imidacloprid and fipronil were accurate in both paddy water and 1 cm deep paddy soil. The coefficient of determination and Nash-Sutcliffe model efficiency were greater than 0.87 and 0.60 respectively. The 95th percentiles of the predicted concentrations of fipronil and imidacloprid indicated that the influence of input uncertainty was minor in paddy water but important in paddy soil. The pesticide deposition rate and the desorption rate from the root zone were identified to be the major contributors to the variation in the predicted concentrations in paddy water and soil. The PCPF-NB model was validated for predicting the fate and transport of NB-applied fipronil and imidacloprid using the BT and AS treatment methods. © 2015 Society of Chemical Industry.

Entropy-Based Importance Measure for Uncertain Model Inputs

In the information theory, entropy is a measure of the uncertainty associated with a random variable. To identify the important variables of a system subjected to many random variables, a novel entropy-based importance measure for random variables is proposed in this paper. The method evaluates the effect of a random variable on the output responses by calculating the change of the entropy value. This technique focuses on the influence of input uncertainty on the entropy of the output responses and can be easily extended to the case taking the correlations among the random variables into consideration. Besides, the effect of a random variable within any partial region of interest can also be evaluated by the proposed global sensitivity indicator. The mathematical properties of the proposed importance measure are investigated and proven in detail. Three simple numerical examples are employed to demonstrate the applicability of the new importance measure, and then a probabilistic risk assessment model is used to demonstrate the engineering application of the importance measure.

Influence of input uncertainty on prediction of within-field pesticide leaching risks

Previous research has suggested that pesticide losses at the field scale can be dominated by a small proportion of the field area. The objective of this study was to investigate whether site-specific applications (i.e. avoiding high-risk areas) at the field scale can contribute to a reduction of pesticide leaching despite uncertainty in the underlying model-based leaching risk map. Using a meta-model of the dual-permeability model MACRO, the annual average pesticide leaching concentrations were estimated for 162 sample sites on a 47 ha field. The procedure was repeated for different scenarios describing different patterns of spatial variation of degradation half-lives and the partition coefficient to soil organic carbon. To account for interpolation uncertainty, maps of predicted pesticide leaching risk were produced by the method of sequential Gaussian simulation. The results of the case study show that larger reductions of predicted leaching were achieved by site-specific application than by that of a comparable uniform dose reduction. Hence, site-specific-applications may be a feasible method to reduce pesticide leaching at the field-scale providing that the model approach gives reasonable estimates of the spatial pattern of pesticide leaching.

A new uncertainty importance measure

Uncertainty in parameters is present in many risk assessment problems and leads to uncertainty in model predictions. In this work, we introduce a global sensitivity indicator which looks at the influence of input uncertainty on the entire output distribution without reference to a specific moment of the output (moment independence) and which can be defined also in the presence of correlations among the parameters. We discuss its mathematical properties and highlight the differences between the present indicator, variance-based uncertainty importance measures and a moment independent sensitivity indicator previously introduced in the literature. Numerical results are discussed with application to the probabilistic risk assessment model on which Iman [A matrix-based approach to uncertainty and sensitivity analysis for fault trees. Risk Anal 1987;7(1):22–33] first introduced uncertainty importance measures.