Baseline Correction¶

Baseline Correction, like in SeismoSignal, consists in

• determining, through regression analysis (least-squares-fit method), the polynomial curve that best fits the time-acceleration pairs of values and then

• subtracting from the actual acceleration values their corresponding counterparts as obtained with the regression-derived equation.

In this manner, spurious baseline trends, usually well noticeable in the displacement time-history obtained from double time-integration of uncorrected acceleration records, are removed from the input motion.

See baselinecorr

In [1]:

import numpy as np
import matplotlib.pyplot as plt
from scipy.integrate import cumulative_trapezoid

import gmspy as gm

# %%
# load "kobe" records
ts, acc = gm.load_gm_examples("Kobe")
dt = ts[1] - ts[0]

# %%
# Obtain uncorrected velocity and displacement sequences by direct integration
vel = cumulative_trapezoid(acc, ts, initial=0)
disp = cumulative_trapezoid(vel, ts, initial=0)
plot_obj_ori = [acc, vel, disp]

# %%
# Obtain corrected time histories by different polynomial degrees
plot_obj_corr = []
degrees = [0, 1, 2, 3]
for i, degree in enumerate(degrees):
    acc_corr, vel_corr, disp_corr = gm.baselinecorr(ts, acc, degree, plot=False)
    plot_obj_corr.append([acc_corr, vel_corr, disp_corr])
colors = ["#037ef3", "#f85a40", "#00c16e", "#7552cc"]
titles = ["acceleration", "velocity", "displacement"]

# %%
# plot figure
fig, axs = plt.subplots(3, 1, figsize=(9, 12), sharex=True)
for j in range(3):
    ax = axs[j]
    ax.plot(ts, plot_obj_ori[j], c="gray", lw=1, alpha=0.6, label="origin")
    for k, degree in enumerate(degrees):
        ax.plot(ts, plot_obj_corr[k][j], c=colors[k], lw=1, label=f"degree={degree}")
    ax.hlines(0, np.min(ts), np.max(ts), lw=0.5, colors="k")
    ax.set_xlim(np.min(ts), np.max(ts))
    ax.grid(False)
    ax.set_ylabel(titles[j], fontsize=15)
    ax.tick_params(labelsize=12)
axs[0].legend(fontsize=12, ncol=5, loc="center", bbox_to_anchor=(0.5, 1.15))
axs[-1].set_xlabel("Time (s)", fontsize=15)
plt.show()

import numpy as np import matplotlib.pyplot as plt from scipy.integrate import cumulative_trapezoid import gmspy as gm # %% # load "kobe" records ts, acc = gm.load_gm_examples("Kobe") dt = ts[1] - ts[0] # %% # Obtain uncorrected velocity and displacement sequences by direct integration vel = cumulative_trapezoid(acc, ts, initial=0) disp = cumulative_trapezoid(vel, ts, initial=0) plot_obj_ori = [acc, vel, disp] # %% # Obtain corrected time histories by different polynomial degrees plot_obj_corr = [] degrees = [0, 1, 2, 3] for i, degree in enumerate(degrees): acc_corr, vel_corr, disp_corr = gm.baselinecorr(ts, acc, degree, plot=False) plot_obj_corr.append([acc_corr, vel_corr, disp_corr]) colors = ["#037ef3", "#f85a40", "#00c16e", "#7552cc"] titles = ["acceleration", "velocity", "displacement"] # %% # plot figure fig, axs = plt.subplots(3, 1, figsize=(9, 12), sharex=True) for j in range(3): ax = axs[j] ax.plot(ts, plot_obj_ori[j], c="gray", lw=1, alpha=0.6, label="origin") for k, degree in enumerate(degrees): ax.plot(ts, plot_obj_corr[k][j], c=colors[k], lw=1, label=f"degree={degree}") ax.hlines(0, np.min(ts), np.max(ts), lw=0.5, colors="k") ax.set_xlim(np.min(ts), np.max(ts)) ax.grid(False) ax.set_ylabel(titles[j], fontsize=15) ax.tick_params(labelsize=12) axs[0].legend(fontsize=12, ncol=5, loc="center", bbox_to_anchor=(0.5, 1.15)) axs[-1].set_xlabel("Time (s)", fontsize=15) plt.show()