2011 IR&D Annual Report

Improving Model Prediction Accuracy by Reducing Uncertainty in Model Components, 18-R8169

Principal Investigators
Davis S. Riha
John M. McFarland
Todd L. Bredbenner
Daniel P. Nicolella
Barron J. Bichon
Don Moravits

Inclusive Dates:  07/01/10 – Current

Background — Numerical models such as finite element analysis are routinely used to predict the performance of engineered systems. Government and industry now routinely rely on model predictions to make such decisions as to when to retire system components, how to extend the life of an aging system, or if a new design will be safe or available. The validity of many models used to predict the performance of existing engineered systems has been assessed through historical data, but this type of validation is not possible for new designs or designs used in different environments. The validation of new models using experiments becomes more difficult and costly as the complexity and reliability requirements increase. For example, a highly reliable aircraft engine component is difficult to test to failure under operating conditions due to the high reliability. In addition, it may be cost prohibitive to actually test an expensive component to failure. Other systems are impractical to test such as the in vivo measurement of performance measures in human subjects or animals. Valid model predictions become increasingly important as the cost, reliability and experimental complexity of the engineered system increases. Therefore, effective approaches for model validation are needed to assess and improve model predictions. A general and consistent approach for model validation has not been developed for complex problems. Determining the uncertainty on the model predictions is a critical element in the validation process and is a main focus of this research.

Approach — The primary objectives of this program are to:

  • Develop model precision methodology for different types of model uncertainties (e.g., model form, limited data) and approaches and methods to compute model component uncertainty and their contribution to the total model uncertainty.

  • Demonstrate the methodologies and approaches by developing validated finite element models of mouse ulnae.

Accomplishments — Variance decomposition methods as described by Saltelli, et al., have been implemented, extended and exercised to model different types of uncertainties and identify their importance to the model prediction uncertainty for the model precision methodology. The approaches were evaluated via the reliability analysis for the deflection of a statically indeterminate beam. The example problem illustrates the distinction between aleatory and epistemic uncertainty, as the aleatory distributions for the model inputs are estimated based on limited sample data, which introduces epistemic uncertainty about the distribution parameters such as the means and standard deviations. It is shown that the variance decomposition approach can successfully identify a data-rich input as having a negligible contribution to variance, even though the deterministic model is highly sensitive to that input.

The model precision methodologies and approaches will be demonstrated during the validation of finite element models of the mouse ulnae. A validated model will be developed for the wild type (WT) mouse to predict strain for an in vivo loading protocol. The validated model will be used to predict strains for the BMP2 conditional knockout mouse (cKO), which has different geometry and material properties. The project team has acquired eight wild type and nine cKO mice for the validation experiments. Material testing, validation experiment and boundary condition calibration test protocols are being developed and finalized.

Figure 1. Finite element models will be developed to simulate the Robling-Turner en vivo experiment (left). The validation and calibration experiments are performed in a micro-CT where geometry, displacements, and bone x-ray density can be measured to obtain the calibration and validation data. The protocol includes imaging the mouse arm in the load stage (lower middle), applying a specific load (upper middle), and converting the unloaded and load image to finite element models (right).

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