josephcslater / mousai Goto Github PK

https://hgomersall.github.io/pyFFTW/pyfftw/builders/builders.html

FFTW is much faster, but license restricted. The code should allow the user to optionally call fftw, but not rely on it.

Further, speedups can be obtained with SciPy as seen at https://blog.mide.com/matlab-vs-python-speed-for-vibration-analysis-free-download

https://www.reddit.com/r/Python/comments/azbdvr/python_decorators_made_simple_part_1/

single harmonic works. With higher, it breaks down. Unknown cause at this time.

def duff_osc_ss(x, params):
    omega = params['omega']
    t = params['cur_time']
    xdot = np.array([[x[1]],[-x[0]-.1*x[0]**3-.1*x[1]+1*sin(omega*t)]])
    return xdot


t, x, e, amps, phases = ms.hb_freq(duff_osc_ss, num_variables = 2, omega = 0.1,
                                   eqform='first_order', num_harmonics=5, num_time_steps=51,             
                                   mask_constant=True, f_rtol = 1e-8)#, f_rtol=1e-8)
time, xc = ms.time_history(t, x)
plt.plot(time, xc.T, label='5 harmonics')

Results in failed start.

num_harmonics =1 works fine. This would be a good fall-back call should convergence fail.

https://pytorch.org/blog/the-torch.fft-module-accelerated-fast-fourier-transforms-with-autograd-in-pyTorch/

In https://josephcslater.github.io/mousai/tutorial/demos/Theory_and_Examples.html
Do you use \ddot{z} or \dot{z} ?

VS

Automated initial guess of proper size (of zeros).

Calculate Jacobian and use eigen solution for guess?

Initial guess is a challenge. Not feasible to be very accurate for hard nonlinearities.

Need to raise exception and create working demo

Form of derivative function should be state space by default. Defaulting fails.

I've started adding an implementation of pseudo-arc length continuation to the code. I've checked it to be working for the SDOF Duffing oscillator. You can have a look at the code in the branch "Nidish" in my fork of the project (https://github.com/Nidish96/mousai/tree/Nidish).
I'll raise a pull request once I'm done qualifying the rest. I'm raising this issue here for any suggestions you may give me. I'm having the following things on my agenda:

• Implement Jacobian through finite-differences for both Frequency domain as well as Time domain user supplied routines
• Qualify the code for MDOF systems
• Switch to a better solver
• Create a time-marching-based Monodromy stability estimation method

Provide details and explanation for structure of function to be called.