How to detect multiple plateaus and ascents and descent in the time-series data using python

Question

Analysing time series data of bike trails, I would like to know the time interval for each plateau,ascent and descent.Sample csv file is uploaded here .

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
from datetime import datetime
import matplotlib.dates as mdates


df = pd.read_csv(r'C:\Data\Sample.csv', parse_dates=['dateTime'])
feature_used='Cycle_Alt'
print("Eliminating null values..")
df=df[df[feature_used].notnull()]

plt.figure(figsize=(8,6))
x=df['dateTime']        
y=df['Cycle_Alt']

plt.plot(x,y,c='b',linestyle=':',label="Altitude")
plt.xticks(rotation='vertical')
plt.gcf().autofmt_xdate()   
plt.legend(loc='best', bbox_to_anchor=(1, 0.5))

This plot provides me with a cross-profile like this.

What could be done to classify the time-series data to detect each plateau,ascent and descent, with the assumption that one may have more variables than presented in the sample.

Answer 1

If you are only interested in identify the plateaus, ascents, and descents in a series, the easy way is to use the numpy.diff function to calculate the n-th discrete difference. Then you can use the numpy.sign to convert the differences to either positive (ascents), zero (plateau), or negative (descents).

An example:

a = np.random.randint(1, 5, 10)
#array([1, 1, 1, 1, 3, 4, 2, 2, 2, 2])

diff = np.diff(a)
#array([ 0,  0,  0,  2,  1, -2,  0,  0,  0])

gradient = np.sign(diff)
#array([ 0,  0,  0,  1,  1, -1,  0,  0,  0])

Note that the final array gradient will have one fewer element than the original array, because the numpy.diff function will return (n-1) differences for an array of length n.

Answer 2

Not exactly what was asked but Google suggests this when searching for a plateau-finding algorithm so I'll leave this here for reference.

When just looking for plateaus, using the diff - cumsum combo to group the data can be very useful, especially when the the given values contain some amount of noise:

import numpy as np
import pandas as pd
from matplotlib import pyplot as plt

if __name__ == '__main__':
    # example data
    df = pd.DataFrame(
        {
            'time': np.arange(0, 8),
            'data': [1, 1.01, 2.0, 2.01, 2.5, 2.7, 3.1, 3.101]}
    )
    plt.plot(
        df['time'], df['data'], label=f"original data",
        marker='x', lw=0.5, ms=2.0, color="black",
    )

    # filter and group plateaus
    max_difference = 0.02
    min_number_points = 2
    # group by maximum difference
    group_ids = (abs(df['data'].diff(1)) > max_difference).cumsum()
    plateau_idx = 0
    for group_idx, group_data in df.groupby(group_ids):
        # filter non-plateaus by min number of points
        if len(group_data) < min_number_points:
            continue
        plateau_idx += 1
        plt.plot(
            group_data['time'], group_data['data'], label=f"Plateau-{plateau_idx}",
            marker='x', lw=1.5, ms=5.0,
        )
        _time = group_data['time'].mean()
        _value = group_data['data'].mean()
        plt.annotate(
            f"Plateau-{plateau_idx}", (_time, _value), ha="center",
        )
    plt.legend()
    plt.show()

A plateau is defined as points that are a maximum of max_difference apart, and contain at least min_number_points .