Optimizing Hybrid Model Parameters in Vortex Studio

The optimization is done via the gradient-free Nelder-Mead method (aka Downhill Simplex algorithm). The code is specified for simulating soil cutting operations (e.g. excavation).

Code structure

|- run.py
|   - constr_nm.py
|       - nelder_mead.py
|           - obj_func.py
|               - input/
|               - ref.py
|       - plot.py
|   - output/
|- test.py

• run.py: Runs the optimization.

  • The initial, lower and upper bounds of optimization variables are defined here.

    X0 = [,]
    LB = [,]
    UB = [,]

  • Some other settings including loading/saving optimal solution, and excavation depth and time can also be set.

    load = True/False
    save = True/False
    depths = [,]  # [m]
    sim_times = [,]  # [sec]

• constr_nm.py: Implements the constrained Nelder-Mead method (reference).

• nelder_mead.py: Implements the Nelder-Mead method (reference).

  • This is modified to terminate the optimization loop when no significant error changes happen (e.g. <1%) during the last specified iterations by setting e.g. history = 10 as fallows:

    if iterations > history+2:
        for i in range(2,history+2):
            fval_sum += abs(fval_history[-1] - fval_history[-i])
        if fval_sum/history < 1:
            break

• obj_func.py: Implements the objective function.

  • The Vortex (excavation) model is called here and implemented in:

    def run_vortex(self, x, depth):
        ...

  • The mean absolute percentage error (MAPE) is calculated using the results from Vortex and experiment.

  • The Vortex files and reference (experimental) results should already be provided in folder input/.

• ref.py: Reads reference (experimental) results from the files provided in input/.

• plot.py: Plots MAPE versus number of function evaluations, and save in folder output/.

• test.py: Tests the Vortex (excavation) model via the optimal solution and saves the results.

Requirements

• VxSim
• numpy
• pickle