How can you ensure your finite element method simulations are sensitive to input parameter changes?

3 How to vary input parameters?

The next step in sensitivity analysis is to vary the input parameters within their feasible ranges and observe the changes in the output of interest. There are a few ways to do this, such as the One-at-a-time (OAT) method, where one parameter is changed at a time while keeping the others fixed. This is simple and intuitive, but may miss interactions and nonlinearities among parameters. The Full factorial method changes all parameters simultaneously at different levels, which is comprehensive and accurate but may require a lot of simulations. The Fractional factorial method changes a subset of parameters simultaneously at different levels, compromising between OAT and Full factorial methods, but introducing aliasing and confounding effects. Lastly, the Monte Carlo method randomly samples parameters from their probability distributions, being flexible and robust, but computationally intensive. You should choose a method that suits your FEM problem, your output of interest, and your available resources.

4 How to measure sensitivity?

The final step in sensitivity analysis is to measure the sensitivity of the output to the input parameters. To do this, you can use different metrics such as absolute or relative change, correlation coefficient, and variance-based methods. Each metric has its own advantages and drawbacks. For example, absolute or relative change is simple and direct, but it may not reflect the overall sensitivity of the output to the input parameter. On the other hand, variance-based methods are comprehensive and rigorous, but they may require a large number of simulations and become mathematically challenging. Therefore, when selecting a metric to measure sensitivity, you should consider the nature and importance of your output and your input parameter.

5 What are some common pitfalls and errors?

Sensitivity analysis is a valuable technique for FEM simulations that can help improve the quality and efficiency of analysis and design, as well as enhance understanding and confidence in FEM results. However, there are potential pitfalls and errors to avoid, such as ignoring uncertainty and variability of input parameters, using inappropriate or unrealistic ranges or distributions for the input parameters, using inadequate or inaccurate output measures, and interpreting sensitivity results without considering the physical meaning, context, and limitations of the FEM problem. To ensure the validity and reliability of your input parameters, output measures, and sensitivity results, it's important to compare them with other sources of information like experimental data, analytical solutions, or expert opinions.