A Spatial-Random-Process Based Multidisciplinary System Uncertainty Propagation Approach With Model Uncertainty

2015 ◽  
Vol 137 (10) ◽  
Author(s):  
Zhen Jiang ◽  
Wei Li ◽  
Daniel W. Apley ◽  
Wei Chen
Keyword(s):  
Uncertainty Quantification ◽  
Random Process ◽  
Model Uncertainty ◽  
Electronic Packaging ◽  
Epistemic Uncertainty ◽  
Uncertainty Propagation ◽  
Statistical Moments ◽  
Robust Design Optimization ◽  
System Uncertainty ◽  
Multidisciplinary System

The performance of a multidisciplinary system is inevitably affected by various sources of uncertainties, usually categorized as aleatory (e.g., input variability) or epistemic (e.g., model uncertainty) uncertainty. In the framework of design under uncertainty, all sources of uncertainties should be aggregated to assess the uncertainty of system quantities of interest (QOIs). In a multidisciplinary design system, uncertainty propagation (UP) refers to the analysis that quantifies the overall uncertainty of system QOIs resulting from all sources of aleatory and epistemic uncertainty originating in the individual disciplines. However, due to the complexity of multidisciplinary simulation, especially the coupling relationships between individual disciplines, many UP approaches in the existing literature only consider aleatory uncertainty and ignore the impact of epistemic uncertainty. In this paper, we address the issue of efficient uncertainty quantification of system QOIs considering both aleatory and epistemic uncertainties. We propose a spatial-random-process (SRP) based multidisciplinary uncertainty analysis (MUA) method that, subsequent to SRP-based disciplinary model uncertainty quantification, fully utilizes the structure of SRP emulators and leads to compact analytical formulas for assessing statistical moments of uncertain QOIs. The proposed method is applied to a benchmark electronic packaging design problem. The estimated low-order statistical moments of the QOIs are compared to the results from Monte Carlo simulations (MCSs) to demonstrate the effectiveness of the method. The UP result is then used to facilitate the robust design optimization of the electronic packaging system.

A System Uncertainty Propagation Approach With Model Uncertainty Quantification in Multidisciplinary Design

2014 ◽  
Author(s):  
Zhen Jiang ◽  
Wei Li ◽  
Daniel W. Apley ◽  
Wei Chen
Keyword(s):  
Uncertainty Quantification ◽  
Model Uncertainty ◽  
Epistemic Uncertainty ◽  
Uncertainty Propagation ◽  
Statistical Moments ◽  
Multidisciplinary Design ◽  
Design System ◽  
System Uncertainty ◽  
The Impact ◽  
Multidisciplinary System

The performance of a multidisciplinary system is inevitably affected by various sources of uncertainties, usually categorized as aleatory (e.g. input variability) or epistemic (e.g. model uncertainty) uncertainty. In the framework of design under uncertainty, all sources of uncertainties should be aggregated to assess the uncertainty of system quantities of interest (QOIs). In a multidisciplinary design system, uncertainty propagation refers to the analysis that quantifies the overall uncertainty of system QOIs resulting from all sources of aleatory and epistemic uncertainty originating in the individual disciplines. However, due to the complexity of multidisciplinary simulation, especially the coupling relationships between individual disciplines, many uncertainty propagation approaches in the existing literature only consider aleatory uncertainty and ignore the impact of epistemic uncertainty. In this paper, we address the issue of efficient uncertainty quantification of system QOIs considering both aleatory and epistemic uncertainties. We propose a spatial-random-process (SRP) based multidisciplinary uncertainty analysis (MUA) method that, subsequent to SRP-based disciplinary model uncertainty quantification, fully utilizes the structure of SRP emulators and leads to compact analytical formulas for assessing statistical moments of uncertain QOIs. The proposed method is applied to a benchmark electronics packaging problem. To demonstrate the effectiveness of the method, the estimated low-order statistical moments of the QOIs are compared to the results from Monte Carlo simulations.

scholarly journals Basic Framework and Main Methods of Uncertainty Quantification

2020 ◽  
Vol 2020 ◽  
pp. 1-18
Author(s):  
Juan Zhang ◽  
Junping Yin ◽  
Ruili Wang
Keyword(s):  
Sensitivity Analysis ◽  
Bayesian Inference ◽  
Uncertainty Quantification ◽  
Model Uncertainty ◽  
Model Calibration ◽  
Uncertainty Propagation ◽  
Propagation Model ◽  
Practical Significance ◽  
The Core ◽  
Basic Framework

Since 2000, the research of uncertainty quantification (UQ) has been successfully applied in many fields and has been highly valued and strongly supported by academia and industry. This review firstly discusses the sources and the types of uncertainties and gives an overall discussion on the goal, practical significance, and basic framework of the research of UQ. Then, the core ideas and typical methods of several important UQ processes are introduced, including sensitivity analysis, uncertainty propagation, model calibration, Bayesian inference, experimental design, surrogate model, and model uncertainty analysis.

scholarly journals Reduction of Epistemic Model Uncertainty in Simulation-Based Multidisciplinary Design

2016 ◽  
Vol 138 (8) ◽  
Author(s):  
Zhen Jiang ◽  
Shishi Chen ◽  
Daniel W. Apley ◽  
Wei Chen
Keyword(s):  
Resource Allocation ◽  
Model Uncertainty ◽  
Epistemic Uncertainty ◽  
Complex Structure ◽  
Data Gathering ◽  
Simulation Models ◽  
Multidisciplinary Design ◽  
Novel Approach ◽  
Multidisciplinary System ◽  
Epistemic Model

Model uncertainty is a significant source of epistemic uncertainty that affects the prediction of a multidisciplinary system. In order to achieve a reliable design, it is critical to ensure that the disciplinary/subsystem simulation models are trustworthy, so that the aggregated uncertainty of system quantities of interest (QOIs) is acceptable. Reduction of model uncertainty can be achieved by gathering additional experiments and simulations data; however, resource allocation for multidisciplinary design optimization (MDO) and analysis remains a challenging task due to the complex structure of the system, which involves decision makings about where (sampling locations), what (disciplinary responses), and which type (simulations versus experiments) for allocating more resources. Instead of trying to concurrently make the above decisions, which would be generally intractable, we develop a novel approach in this paper to break the decision making into a sequential procedure. First, a multidisciplinary uncertainty analysis (MUA) is developed to identify the input settings with unacceptable amounts of uncertainty with respect to the system QOIs. Next, a multidisciplinary statistical sensitivity analysis (MSSA) is developed to investigate the relative contributions of (functional) disciplinary responses to the uncertainty of system QOIs. The input settings and critical responses to allocate resources are selected based on the results from MUA and MSSA, with the aid of a new correlation analysis derived from spatial-random-process (SRP) modeling concepts, ensuring the sparsity of the selected inputs. Finally, an enhanced preposterior analysis predicts the effectiveness of allocating experimental and/or computational resource to answer the question about which type of resource to allocate. The proposed method is applied to a benchmark electronic packaging problem to demonstrate how epistemic model uncertainty is gradually reduced via resource allocation for data gathering.

Uncertainty Analysis in Fatigue Life Prediction of Concrete Using Evidence Theory

2016 ◽  
Vol 866 ◽  
pp. 25-30
Author(s):  
He Sheng Tang ◽  
Jia He Mei ◽  
Wei Chen ◽  
Da Wei Li ◽  
Song Tao Xue
Keyword(s):  
Experimental Data ◽  
Fatigue Life ◽  
Uncertainty Analysis ◽  
Model Uncertainty ◽  
Life Prediction ◽  
Epistemic Uncertainty ◽  
Uncertainty Propagation ◽  
Evidence Theory ◽  
Fatigue Life Prediction ◽  
Theory Method

Various sources of uncertainty exist in concrete fatigue life prediction, such as variability in loading conditions, material parameters, experimental data and model uncertainty. In this article, the uncertainty model of concrete fatigue life prediction based on the S-N curve is built, and the evidence theory method is presented for uncertainty analysis in fatigue life prediction of concrete while considering the epistemic uncertainty of the parameter of the model. Based on the experimental of concrete four-point bending beams, the evidence theory method is applied to quantify the epistemic uncertainty stem from experimental data and model uncertainty. To improve the efficiency of computation, a method of differential evolution is adopted to speedup the works of uncertainty propagation. The efficiency and feasibility of the proposed approach are verified through a comparative analysis of probability theory.

scholarly journals Stochastic and epistemic uncertainty propagation in LCA

2013 ◽  
Vol 18 (7) ◽  
pp. 1393-1403 ◽  
Author(s):  
Julie Clavreul ◽  
Dominique Guyonnet ◽  
Davide Tonini ◽  
Thomas H. Christensen
Keyword(s):  
Epistemic Uncertainty ◽  
Uncertainty Propagation

Comparative Analysis of Methodologies for Uncertainty Propagation and Quantification

2017 ◽  
Author(s):  
Alessandra Cuneo ◽  
Alberto Traverso ◽  
Shahrokh Shahpar
Keyword(s):  
Engineering Design ◽  
Polynomial Chaos ◽  
Epistemic Uncertainty ◽  
Uncertainty Propagation ◽  
Computational Cost ◽  
Computational Effort ◽  
Optimization Under Uncertainty ◽  
Design Parameters ◽  
Test Case ◽  
Aleatory And Epistemic Uncertainty

In engineering design, uncertainty is inevitable and can cause a significant deviation in the performance of a system. Uncertainty in input parameters can be categorized into two groups: aleatory and epistemic uncertainty. The work presented here is focused on aleatory uncertainty, which can cause natural, unpredictable and uncontrollable variations in performance of the system under study. Such uncertainty can be quantified using statistical methods, but the main obstacle is often the computational cost, because the representative model is typically highly non-linear and complex. Therefore, it is necessary to have a robust tool that can perform the uncertainty propagation with as few evaluations as possible. In the last few years, different methodologies for uncertainty propagation and quantification have been proposed. The focus of this study is to evaluate four different methods to demonstrate strengths and weaknesses of each approach. The first method considered is Monte Carlo simulation, a sampling method that can give high accuracy but needs a relatively large computational effort. The second method is Polynomial Chaos, an approximated method where the probabilistic parameters of the response function are modelled with orthogonal polynomials. The third method considered is Mid-range Approximation Method. This approach is based on the assembly of multiple meta-models into one model to perform optimization under uncertainty. The fourth method is the application of the first two methods not directly to the model but to a response surface representing the model of the simulation, to decrease computational cost. All these methods have been applied to a set of analytical test functions and engineering test cases. Relevant aspects of the engineering design and analysis such as high number of stochastic variables and optimised design problem with and without stochastic design parameters were assessed. Polynomial Chaos emerges as the most promising methodology, and was then applied to a turbomachinery test case based on a thermal analysis of a high-pressure turbine disk.

Optimization of a Centrifugal Compressor Impeller Design for Robustness to Manufacturing Uncertainties

2013 ◽  
Author(s):  
A. Javed ◽  
R. Pecnik ◽  
J. P. van Buijtenen
Keyword(s):  
Sensitivity Analysis ◽  
Surrogate Model ◽  
Uncertainty Propagation ◽  
Computational Cost ◽  
Dimensional Accuracy ◽  
Robust Design Optimization ◽  
Centrifugal Impeller ◽  
Conceptual Design Phase ◽  
Compressor Impeller ◽  
High Production Cost

Compressor impellers for mass-market turbochargers are die-casted and machined with an aim to achieve high dimensional accuracy and acquire specific performance. However, manufacturing uncertainties result in dimensional deviations causing incompatible operational performance and assembly errors. Process capability limitations of the manufacturer can cause an increase in part rejections, resulting in high production cost. This paper presents a study on a centrifugal impeller with focus on the conceptual design phase to obtain a turbomachine that is robust to manufacturing uncertainties. The impeller has been parameterized and evaluated using a commercial computational fluid dynamics (CFD) solver. Considering the computational cost of CFD, a surrogate model has been prepared for the impeller by response surface methodology (RSM) using space-filling Latin hypercube designs. A sensitivity analysis has been performed initially to identify the critical geometric parameters which influence the performance mainly. Sensitivity analysis is followed by the uncertainty propagation and quantification using the surrogate model based Monte Carlo simulation. Finally a robust design optimization has been carried out using a stochastic optimization algorithm leading to a robust impeller design for which the performance is relatively insensitive to variability in geometry without reducing the sources of inherent variation i.e. the manufacturing noise.

Possibilistic Uncertainty Quantification in 1-D Consolidation Problems

2021 ◽  
Author(s):  
Djamalddine Boumezerane
Keyword(s):  
Uncertainty Quantification ◽  
Probability Distributions ◽  
Uncertainty Propagation ◽  
Possibility Distribution ◽  
Coefficient Of Consolidation ◽  
Consolidation Process ◽  
Possibility Distributions ◽  
Coverage Function ◽  
The One ◽  
Measure Of Uncertainty

Abstract In this study, we use possibility distribution as a basis for parameter uncertainty quantification in one-dimensional consolidation problems. A Possibility distribution is the one-point coverage function of a random set and viewed as containing both partial ignorance and uncertainty. Vagueness and scarcity of information needed for characterizing the coefficient of consolidation in clay can be handled using possibility distributions. Possibility distributions can be constructed from existing data, or based on transformation of probability distributions. An attempt is made to set a systematic approach for estimating uncertainty propagation during the consolidation process. The measure of uncertainty is based on Klir's definition (1995). We make comparisons with results obtained from other approaches (probabilistic…) and discuss the importance of using possibility distributions in this type of problems.

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