Analyzing Propagation of Model Form Uncertainty for Different Suspension Strut Models

In modeling and simulation, model-form uncertainty arises from the lack of knowledge and simplification during modeling process and numerical treatment for ease of computation. Traditional uncertainty quantification approaches are based on assumptions of stochasticity in real, reciprocal, or functional spaces to make them computationally tractable. This makes the prediction of important quantities of interest such as rare events difficult. In this paper, a new approach to capture model-form uncertainty is proposed. It is based on fractional calculus, and its flexibility allows us to model a family of non-Gaussian processes, which provides a more generic description of the physical world. A generalized fractional Fokker-Planck equation (fFPE) is proposed to describe the drift-diffusion processes under long-range correlations and memory effects. A new model calibration approach based on the maximum accumulative mutual information is also proposed to reduce model-form uncertainty, where an optimization procedure is taken.

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Probability Bounds Analysis Applied to the Sandia Verification and Validation Challenge Problem

Journal of Verification Validation and Uncertainty Quantification ◽

10.1115/1.4031285 ◽

2016 ◽

Vol 1 (1) ◽

Cited By ~ 10

Author(s):

Aniruddha Choudhary ◽

Ian T. Voyles ◽

Christopher J. Roy ◽

William L. Oberkampf ◽

Mayuresh Patil

Keyword(s):

Experimental Data ◽

Physical Nature ◽

Distribution Functions ◽

Verification And Validation ◽

Cumulative Distribution ◽

Probability Bounds ◽

Model Form ◽

Interval Representation ◽

Model Predictions ◽

True System

Our approach to the Sandia Verification and Validation Challenge Problem is to use probability bounds analysis (PBA) based on probabilistic representation for aleatory uncertainties and interval representation for (most) epistemic uncertainties. The nondeterministic model predictions thus take the form of p-boxes, or bounding cumulative distribution functions (CDFs) that contain all possible families of CDFs that could exist within the uncertainty bounds. The scarcity of experimental data provides little support for treatment of all uncertain inputs as purely aleatory uncertainties and also precludes significant calibration of the models. We instead seek to estimate the model form uncertainty at conditions where the experimental data are available, then extrapolate this uncertainty to conditions where no data exist. The modified area validation metric (MAVM) is employed to estimate the model form uncertainty which is important because the model involves significant simplifications (both geometric and physical nature) of the true system. The results of verification and validation processes are treated as additional interval-based uncertainties applied to the nondeterministic model predictions based on which the failure prediction is made. Based on the method employed, we estimate the probability of failure to be as large as 0.0034, concluding that the tanks are unsafe.

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Centralized Model Form

Tensor Product Model Transformation in Polytopic Model-Based Control ◽

10.1201/9781315218045-12 ◽

2018 ◽

pp. 105-112

Keyword(s):

Model Form ◽

Centralized Model

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