python - 一维数据中的锐步检测

Question

我的问题基本上分为两部分。我有一个一维数据集，一方面我想平滑以消除噪声，另一方面我想在数据中非常精确地检测（大）步骤。

1）关于步数检测部分，我已经在这里找到了一个有趣的条目在一维数据中进行步数检测，但这种方法似乎不适用于我的数据。

所以我的原始数据看起来像： 在此处输入图像描述

当我应用上述方法时，结果如下： 在此处输入图像描述

2）关于数据平滑部分，我已经尝试了一些数据平滑，比如应用 scipy 中的 gaussian_filter1d。但是当然，我的数据越平滑，检测到的步骤就越不精确（或者我在这部分错了吗？）。有没有更好的方法来平滑数据但保持步骤清晰？

原始数据将是：

[441.0, 414.0, 389.0, 430.0, 403.0, 402.0, 475.0, 417.0, 535.0, 476.0, 461.0, 415.0, 476.0, 442.0, 411.0, 422.0, 417.0, 451.0, 428.0, 455.0, 446.0, 414.0, 411.0, 413.0, 412.0, 424.0, 454.0, 439.0, 422.0, 417.0, 449.0, 417.0, 445.0, 411.0, 388.0, 420.0, 432.0, 457.0, 421.0, 415.0, 486.0, 449.0, 419.0, 453.0, 424.0, 451.0, 432.0, 464.0, 430.0, 469.0, 404.0, 461.0, 443.0, 440.0, 407.0, 452.0, 424.0, 426.0, 451.0, 423.0, 479.0, 407.0, 419.0, 435.0, 463.0, 455.0, 420.0, 413.0, 441.0, 451.0, 398.0, 433.0, 449.0, 451.0, 441.0, 450.0, 412.0, 440.0, 419.0, 408.0, 393.0, 395.0, 409.0, 450.0, 416.0, 398.0, 443.0, 403.0, 420.0, 411.0, 397.0, 416.0, 455.0, 392.0, 441.0, 422.0, 398.0, 445.0, 491.0, 405.0, 410.0, 381.0, 427.0, 403.0, 408.0, 427.0, 441.0, 464.0, 429.0, 420.0, 463.0, 405.0, 422.0, 408.0, 421.0, 464.0, 442.0, 429.0, 477.0, 407.0, 438.0, 453.0, 359.0, 435.0, 452.0, 443.0, 371.0, 503.0, 464.0, 466.0, 446.0, 465.0, 409.0, 440.0, 415.0, 384.0, 462.0, 446.0, 454.0, 440.0, 490.0, 400.0, 430.0, 416.0, 466.0, 436.0, 451.0, 408.0, 423.0, 449.0, 396.0, 417.0, 409.0, 446.0, 408.0, 426.0, 401.0, 417.0, 410.0, 361.0, 381.0, 416.0, 443.0, 413.0, 449.0, 411.0, 425.0, 439.0, 392.0, 464.0, 432.0, 387.0, 408.0, 454.0, 455.0, 449.0, 420.0, 379.0, 446.0, 400.0, 436.0, 461.0, 451.0, 433.0, 417.0, 415.0, 449.0, 397.0, 390.0, 381.0, 416.0, 411.0, 407.0, 420.0, 474.0, 444.0, 390.0, 413.0, 410.0, 428.0, 425.0, 405.0, 398.0, 406.0, 431.0, 420.0, 468.0, 463.0, 431.0, 415.0, 381.0, 427.0, 438.0, 431.0, 388.0, 440.0, 467.0, 453.0, 441.0, 373.0, 418.0, 450.0, 395.0, 407.0, 433.0, 425.0, 462.0, 392.0, 424.0, 435.0, 429.0, 409.0, 430.0, 410.0, 394.0, 407.0, 412.0, 420.0, 432.0, 419.0, 415.0, 338.0, 397.0, 436.0, 422.0, 409.0, 431.0, 422.0, 437.0, 377.0, 493.0, 417.0, 416.0, 468.0, 468.0, 428.0, 459.0, 410.0, 462.0, 391.0, 433.0, 410.0, 388.0, 397.0, 421.0, 416.0, 429.0, 410.0, 447.0, 368.0, 397.0, 405.0, 421.0, 393.0, 446.0, 404.0, 414.0, 418.0, 426.0, 408.0, 389.0, 426.0, 442.0, 476.0, 409.0, 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提前谢谢了！

标签： pythonsignal-processing

Answer 1

您可以在处理中添加进一步的步骤并检测卷积数据的局部最大值，而不仅仅是单个最大值点。

一种方法是使用scipy.signal.find_peaks

通过构建卷积方法，您可以添加find_peaks如下所示的步骤：

import numpy as np
from scipy import signal
from matplotlib import pyplot as plt

d = [ your data ]

# Convolution part
dary = np.array(d)
dary -= np.average(dary)

step = np.hstack((np.ones(len(dary)), -1*np.ones(len(dary))))

dary_step = np.convolve(dary, step, mode='valid')

# Get the peaks of the convolution
peaks = signal.find_peaks(dary_step, width=20)[0]

# plots
plt.figure()

plt.plot(dary)

plt.plot(dary_step/10)

for ii in range(len(peaks)):
    plt.plot((peaks[ii], peaks[ii]), (-1500, 1500), 'r')

plt.show()

这将呈现输出：

上述方法找到向上的步骤，而您可以通过简单地使用scipy.signal.find_peaks(-dary_step)- 找到向下的步骤 - 正如评论中所建议的那样。