Monte Carlo Simulation a statistical method which uses simulation to model the probability of outcomes of a complex model whose behaviour cannot be easily determined due to a vast number of variables. Transducer performance is affected by a number of design variables.
In this example we vary both the PZT thickness and the matching layer thickness of a transducer to get a better idea of the design space and how the key performance (KPIs) relate to these inputs.
A schematic of the model and the two input variables can be seen below:
The key model parameters were as follows. PZT thickness and matching layer thickness are set as design variables to be randomly varied (indicated by *)
|Design Variable||Description||Default Value|
|pzt_rad||PZT radius||60 mm|
|pzt_thk *||PZT thickness||10 mm|
|thkMat *||Matching layer thickness||3.2 mm|
|back||Backing thickness||30 mm|
|water||Water thickness||50 mm|
|steel||Reflector thickness||40 mm|
|gap||Housing width||30 mm|
1000 random input variables were created with the following constraints:
- PZT thickness: 10 mm ± 4%
- Matching thickness: 3.2 mm ± 3.125%
Monte Carlo Results
The full study was completed in 11 minutes when using 16 cores per simulation and had a total cost of 31.47 Core-Hours.
Using the outputs from the simulations, it is possible to calculate the KPIs such as centre frequency, sensitivity and frequency bandwidth. The inputs and outputs can then be plot in a number of ways to get insight into the device performance. Results are plotted below in MATLAB.
Try this Yourself
To run this Monte Carlo study you will need to download the OnScale and MATLAB files.
- Extract all of the files from the downloaded folder
- Open 'monte_carlo_pre_v1.m' and select run
- Open OnScale and Select Cloud Scheduler
- Select 'PZT_2D.flxinp' as the input file
- Under Parametric Sweep, select User Defined Variable File from the dropdown
- Next to Input Files, select ... and open 'simdata.csv'
- Select Estimate + Run
- Download all *.flxhst files
- Open 'mat_fft.revinp'
- Insert the name of the directory which your files were downloaded to into the variable tdir
- Select Run
- Open 'monte_carlo_post_v1.m' and select Run