Example1 - Getting started

This example is intended to show the basic usage of the package, and how to run a simple analysis with it, the example is taken from [C81](#ref-1) and represents a 5 story shear-type building..

To access the data and the exact results of the system we can call the example_data() function under the submodule functions.gen, which will return a tuple where the first output is an array representing the acceleration time histories of the system (subject to white noise excitation), and the second output is a tuple containing the exact result in terms of modal parameters (natural frequencies, mode shapes and damping ratios) obtained from the modal analysis of the system.

import os
import sys
import numpy as np
# Add the directory we execute the script from to path:
sys.path.insert(0, os.path.realpath('__file__'))

# import the function to generate the example dataset
from pyoma2.functions.gen import example_data

# generate example data and results
data, ground_truth = example_data()

# Print the exact results
np.set_printoptions(precision=3)
print(f"the natural frequencies are: {ground_truth[0]} \n")
print(f"the damping is: {ground_truth[2]} \n")
print("the (column-wise) mode shape matrix: \n"
f"{ground_truth[1]} \n")

>>> the natural frequencies are: [0.89  2.598 4.095 5.261 6.   ]
>>> the damping is: 0.02
>>> the (column-wise) mode shape matrix:
    [[ 0.285 -0.764  1.     0.919 -0.546]
    [ 0.546 -1.     0.285 -0.764  0.919]
    [ 0.764 -0.546 -0.919 -0.285 -1.   ]
    [ 0.919  0.285 -0.546  1.     0.764]
    [ 1.     0.919  0.764 -0.546 -0.285]]

Now we can instantiate the SingleSetup class, passing the dataset and the sampling frequency as arguments

from pyoma2.setup.single import SingleSetup

simp_5dof = SingleSetup(data, fs=600)

Since the maximum frequency is at approximately 6Hz, we can decimate the signal quite a bit. To do this we can call the decimate_data() method

# Decimate the data
simp_5dof.decimate_data(q=30)

To analise the data we need to instanciate the desired algorithm to use with a name and the required arguments.

from pyoma2.algorithms.fdd import FDD
from pyoma2.algorithms.ssi import SSIdat

# Initialise the algorithms
fdd = FDD(name="FDD", nxseg=1024, method_SD="cor")
ssidat = SSIdat(name="SSIdat", br=30, ordmax=30)

# Add algorithms to the class
simp_5dof.add_algorithms(fdd, ssidat)

# run
simp_5dof.run_all()

We can now check the results

# plot singular values of the spectral density matrix
_, _ = fdd.plot_CMIF(freqlim=(0,8))

# plot the stabilisation diagram
_, _ = ssidat.plot_stab(freqlim=(0,10),hide_poles=False)
_images/Ex1-Fig1.png _images/Ex1-Fig2.png

We can get the modal parameters with the help of an interactive plot calling the mpe_from_plot() method, or we can get the results “manually” with the mpe() method.

# get the modal parameters with the interactive plot
# simp_ex.mpe_from_plot("SSIdat", freqlim=(0,10))

# or manually
simp_5dof.mpe("SSIdat", sel_freq=[0.89, 2.598, 4.095, 5.261, 6.], order_in="find_min")

Now we can access all the results and compare them to the exact values.

# dict of results
ssidat_res = dict(ssidat.result)

from pyoma2.functions.plot import plot_mac_matrix

# print the results
print(f"order out: {ssidat_res['order_out']} \n")
print(f"the natural frequencies are: {ssidat_res['Fn']} \n")
print(f"the dampings are: {ssidat_res['Xi']} \n")
print("the (column-wise) mode shape matrix:")
print(f"{ssidat_res['Phi'].real} \n")
_, _ = plot_mac_matrix(ssidat_res['Phi'].real, ground_truth[1])

>>> the natural frequencies are: [0.891 2.596 4.097 5.263 5.998]
>>> the dampings are: [0.022 0.019 0.025 0.019 0.019]
>>> the (column-wise) mode shape matrix:
    [[ 0.312  0.773  1.     0.926  0.537]
    [ 0.545  1.     0.279 -0.762 -0.912]
    [ 0.774  0.541 -0.912 -0.283  1.   ]
    [ 0.985 -0.285 -0.534  1.    -0.738]
    [ 1.    -0.942  0.749 -0.544  0.279]]
_images/Ex1-Fig3.png