Research Papers

Definition and Implementation of a Method for Uncertainty Aggregation in Component-Based System Simulation Models

[+] Author and Article Information
Magnus Eek

Vehicle Systems,
Saab Aeronautics,
Linköping SE-581 88, Sweden
e-mail: magnus.eek@saabgroup.com

Hampus Gavel

Aeronautical Engineering & Weapons,
Saab Aeronautics,
Linköping SE-581 88, Sweden
e-mail: hampus.gavel@saabgroup.com

Johan Ölvander

Division of Machine Design,
Department of Management and Engineering,
Linköping University,
Linköping SE-581 83, Sweden
e-mail: johan.olvander@liu.se

1Corresponding author.

Manuscript received November 13, 2015; final manuscript received December 23, 2016; published online February 6, 2017. Assoc. Editor: Kevin Dowding.

J. Verif. Valid. Uncert 2(1), 011004 (Feb 06, 2017) (12 pages) Paper No: VVUQ-15-1053; doi: 10.1115/1.4035716 History: Received November 13, 2015; Revised December 23, 2016

Component-based system simulation models are used throughout all development phases for design and verification of both physical systems and control software, not least in the aeronautical industry. However, the application of structured methods for uncertainty quantification (UQ) of system simulation models is rarely seen. To enable dimensionality reduction of a UQ problem and to thereby make UQ more feasible for industry-grade system simulation models, this paper describes a pragmatic method for uncertainty aggregation. The central idea of the proposed aggregation method is to integrate information obtained during common practice component-level validation directly into the components, and to utilize this information in model-level UQ. A generic component output uncertainty description has been defined and implemented in a Modelica library for modeling and simulation (M&S) of aircraft vehicle systems. An example is provided on how to characterize and quantify a component's aggregated output uncertainty based on the component-level bench test measurement data. Furthermore, the industrial applicability of the uncertainty aggregation method is demonstrated in an approximate UQ of an aircraft liquid cooling system simulation model. For cases when the concept of thorough UQ resulting in probability boxes is not feasible, the demonstrated approximate UQ using aggregated uncertainties is considered to be a pragmatic alternative fairly in reach for the common M&S practitioner within the area of system simulation.

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Fig. 1

Classification of modeling approaches

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Fig. 2

Graphical view of the radar liquid cooling simulation model

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Fig. 3

Process for specification, development, and V&V of a simulation model, supported by UQ using the component output uncertainty method. The original workflow described in Ref. [24] is here detailed in terms of possible input data used and extended with two additional dash-masked steps showing the concept of using the component output uncertainty method to support the traditional model validation against the measurement data. The dashed activities represent the UQ, and the dashed arrows indicate that the UQ make use of data from the component-level validation and is a support to the model-level validation.

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Fig. 4

A new uncertain component (dashed) based on an original component (in this case a pipe component) connected with an uncertainty description component (here named UC). The original component's nominal pressure drop Δpcomponent is shown, as well as the added uncertainty in the pressure drop ΔpUC.

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Fig. 5

Left: Simulation results for a ±50% variation of the pressure uncertainty parameter of a pipe component with relative output uncertainty. Right: Simulation results for a ±50% variation of the temperature uncertainty parameter of a pipe component with relative output uncertainty.

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Fig. 6

Left: Simulation results plotted together with the measurement data. Each dot represents a steady-state measurement point, and each circle represents a simulation result for the corresponding boundary conditions. Right: The residual E for varying mass flow, computed from S and D with corresponding boundary conditions.

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Fig. 7

Histogram representing the estimated relative output uncertainty (URUC) of the pump's pressure difference

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Fig. 8

Mean value comparison of heat load inlet pressure and temperature using Monte Carlo sampling and LHS, respectively

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Fig. 9

Resulting PDF and CDF for the heat load inlet pressure using Monte Carlo sampling and LHS, respectively

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Fig. 10

LHS 250 intervals; scatter plots including result from the linear regression, R2-values in title of each subplot

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Fig. 11

Monte Carlo, 1.5 × ·105 samples; scatter plots including the result from linear regression, R2-values in title of each subplot




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