In dynamic system modeling, understanding how input parameters influence model behaviour is essential for improving accuracy, reliability, and design efficiency. Global Sensitivity Analysis (GSA) is a powerful method that quantifies the impact of each parameter on model outputs, capturing both direct effects and interactions.
Built-In Sensitivity Tools in Dymola 2025x Refresh 1
With the release of Dymola 2025x Refresh 1, GSA is now a built-in feature, enabling users to perform detailed sensitivity studies directly within the software. This update supports multiple approaches, including Monte Carlo sampling, Sobol indices, and the newly added Latin Hypercube sampling, making it easier to explore complex parameter relationships.
Monte Carlo and Sobol Sensitivity Analysis Explained
Monte Carlo simulation involves randomly sampling input parameters within defined ranges and running the model repeatedly to observe output variations. For a model defined as:
Y = f(X1, X2, …, Xn)
Monte Carlo helps identify which inputs most significantly affect the output Y. Monte Carlo works by randomly picking values for each input within their ranges and running the model many times. By looking at how Y changes across these runs, we can identify which inputs have the biggest effect.
Sobol indices take this further by decomposing the output variance:
- First-order index (Si): Effect of one input alone.
- Total-order index (STi): Effect of one input plus its interactions.
Formulas:
First Order index Si = variation due to Xi / total variation of Y
Total index STi = variation due to Xi and interactions / total variation of Y
Sensitivity Analysis in a Thermal Model
To demonstrate GSA, we use a simple thermal model with three parameters:
- Q: Constant heat input
- G: Thermal conductance
- C: Thermal capacitance
The observed variable is the temperature T of a heat capacitor over time. This model is intentionally simple, with only three key parameters, but it still captures the essential behaviour of thermal systems. Using global sensitivity analysis, we can measure how changes in Q, G, and C affect the temperature and determine which parameters have the strongest influence across their full range.
Setting Up Sensitivity Analysis in Dymola
Users can access the sensitivity analysis interface via: Design > Randomization > Analysis > SensitivityAnalysis
This interface lets you set up a global sensitivity analysis using the Sobol method with Monte Carlo sampling. Latin Hypercube sampling method is also new with Dymola 2025x Refresh 1. The main setting is the number of random samples, which determines how many parameter combinations are tested to calculate the first-order and total-order Sobol indices.
In our example, uniform distributions were used for G, C, and Q. The observed variable was set to heatCapacitor.T, with a simulation stop time of 3000.
Results: Sensitivity of heatCapacitor.T
| Uncertain Parameter | Observed Variable | First-Order Sensitivity (S₁) | Total-Order Sensitivity (S_T) |
|---|---|---|---|
| G | heatCapacitor.T | -0.0313 | 0.1387 |
| C | heatCapacitor.T | 0.7095 | 0.8871 |
| Q_flow | heatCapacitor.T | 0.1459 | 0.3684 |
- C (thermal capacitance) has the largest impact.
- Q_flow shows moderate impact, mainly through interactions.
- G (conductance) has minimal influence.
Conclusion
Global Sensitivity Analysis in Dymola 2025x empowers engineers to identify key parameters affecting model behaviour. By leveraging Monte Carlo, Sobol indices, and Latin Hypercube sampling, users can enhance model accuracy and design robustness. The built-in tools streamline the process, making GSA accessible and efficient.
For further details, refer to page 1189 of the Dymola full manual for Dymola 2025x Refresh 1.
Written by: Kadir Sahin – Project Engineer
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