Sensitivity Analysis, Uncertainty Propagation, and Validation for Computational Models


Computational modeling is becoming more prevalent in the engineering analysis and design process. This increased reliance means that one must understand the accuracy of the computational models. A first step in understanding the accuracy is to identify the model input parameters for which the computational model is most sensitive. The course will specifically focus on the following techniques for determining sensitivity information: differentiation of analytical models, finite difference of computational models, complex step method, software differentiation, sensitivity equation methods, adjoint methods, and sampling methods (Monte Carlo and Latin Hypercube). Techniques for propagating uncertainty in model inputs through computational models will also be presented. Uncertainty propagation techniques that use the sensitivity information (first-order techniques) and more general techniques based on sampling are covered in the course. The final topic covered is validation of computational models. Validation is a process to assess the accuracy of computational models by comparing to experimental data.

Key Topics:

  • Insights and application of sensitivity analysis
  • Approaches for computing sensitivity coefficients
  • Uncertainty propagation through computational models
  • Sampling-based methods for propagating uncertainty and performing sensitivity analysis
  • Methodology for validation of computational models

Who Should Attend:

This course is intended for engineering analysts that are faced with determining the sensitivity of computational models to parameters in their models. The minimum background is a BS in engineering (or related field). Managers directing the activities of staff responsible for sensitivity analysis would also benefit from this course.

Course Information:

Type of Course: Instructor-Led Short Course
Course Level: Fundamentals/Intermediate
Course Length: 2 days
AIAA CEU's available: Yes



I. Introduction

II. Overview of techniques for computing sensitivity
a. Differentiation of analytical models
b. Impact of sensitivity on conceptual design of a thermal diffusivity experiment
c. Finite difference determination of sensitivity information
d. Software differentiation for computing sensitivity
e. Complex step method for computing sensitivity
f. Sensitivity equation method

III. Uncertainty propagation through computational models
a. Propagation of variance equation
b. Examples demonstrating uncertainty propagation

IV. Sampling methods for uncertainty propagation
a. Monte Carlo sampling based method
b. Latin Hypercube sampling based method
c. Comparison of various methods
d. Example for applying sampling-based approaches

V. Reliability-based approach for uncertainty propagation
a. Method description
i. Demonstration example

VI. Advanced uncertainty topics
a. Correlated Uncertainties
b. Uncertainty propagation for large computational models

VII. Validation of computational models
a. Verification and Validation Concepts
b. Verification and Validation Standards
c. Practical examples from our work experiences



Dr. Kevin Dowding is a Principle Member of the technical staff at Sandia National Laboratories. He has worked the past 15 years on sensitivity analysis, uncertainty analysis, and the interaction of computational models with experiments. He is a member of AIAA and ASME.


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