Multi-Layer Transducer Monte Carlo Study

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.

Model Setup

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.

Input autocorrelation
KPI autocorrelation
Correlation between inputs and KPIs

Try this Yourself

 To run this Monte Carlo study you will need to download the OnScale and MATLAB files. 

Download: Monte Carlo Files

  1. Extract all of the files from the downloaded folder
  2. Open 'monte_carlo_pre_v1.m' and select run
  3. Open OnScale and Select Cloud Scheduler 
  4. Select 'PZT_2D.flxinp' as the input file
  5. Under Parametric Sweep, select User Defined Variable File from the dropdown
  6. Next to Input Files, select ... and open 'simdata.csv'
  7. Select Estimate + Run
  8. Download all *.flxhst files 
  9. Open 'mat_fft.revinp'
  10. Insert the name of the directory which your files were downloaded to into the variable tdir
  11. Select Run
  12. Open 'monte_carlo_post_v1.m' and select Run