What does "simsd" function do?
The "simsd" function simulates linear models using the Monte Carlo method. It performs multiple simulations using different values of the uncertain parameters of the model, and different realizations simulation initial conditions.
What is Monte Carlo method?
The Monte Carlo method is a statistical technique used to understand the impact of risk and uncertainty in prediction and forecasting models. It relies on repeated random sampling to obtain numerical results and is often used in physical and mathematical problems where an analytical solution is difficult or impossible to obtain.
Key Features of the Monte Carlo Method:
- Random Sampling: The core idea is to use randomness to solve problems that might be deterministic in principle. By generating a large number of random samples, you can model the probability of different outcomes in a process that cannot easily be predicted due to the intervention of random variables.
- Simulation: Monte Carlo simulations involve creating a computational model that simulates the process or system being studied. This model is run many times, each time using different randomly generated inputs.
- Statistical Analysis: After running the simulations, the results are analyzed statistically. This can include calculating averages, variances and confidence intervals to understand the behavior of the system.
Please go throwgh the resource linked below to understand more about Monte Carlo Simulation
How does "simsd" work, as I understand it?
- Model Setup: You define a Simulink model with uncertain parameters. These parameters are specified with their nominal values and associated uncertainties (e.g., standard deviation or range).
- Sampling: The simsd function generates samples of these parameters based on their specified distributions. This is akin to performing a Monte Carlo simulation.
- Simulation: For each set of sampled parameters, the Simulink model is simulated to compute the output.
- Analysis: The results from multiple simulations are analyzed to determine the sensitivity of the outputs to the inputs and to quantify the uncertainty in the outputs.
From the documentation for simsd, there are several examples demonstrating its use. Simply run these commands in the MATLAB Command Window:
- >> openExample('ident/SimulateStateSpaceModelUsingMonteCarloMethodExample')
- >> openExample('ident/SimulateEstimatedModelUsingMonteCarloMethodExample')
You can explore more on the documentation page for the function
Please let me know if you have any other difficulties understanding, and I will be glad to assist you.
I hope this helps.
