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.

**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