klippain-shaketune-telegramm/K-ShakeTune/scripts/graph_vibrations.py

#!/usr/bin/env python3

##################################################
#### DIRECTIONAL VIBRATIONS PLOTTING SCRIPT ######
##################################################
# Written by Frix_x#0161 #

# Be sure to make this script executable using SSH: type 'chmod +x ./graph_dir_vibrations.py' when in the folder !

#####################################################################
################ !!! DO NOT EDIT BELOW THIS LINE !!! ################
#####################################################################

import math
import optparse, matplotlib, re, os
from datetime import datetime
from collections import defaultdict
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.font_manager, matplotlib.ticker, matplotlib.gridspec


matplotlib.use('Agg')

from locale_utils import set_locale, print_with_c_locale
from common_func import get_git_version, parse_log, setup_klipper_import, identify_low_energy_zones, compute_curve_similarity_factor, compute_mechanical_parameters, detect_peaks


PEAKS_DETECTION_THRESHOLD = 0.05
PEAKS_RELATIVE_HEIGHT_THRESHOLD = 0.04
CURVE_SIMILARITY_SIGMOID_K = 0.5
SPEEDS_VALLEY_DETECTION_THRESHOLD = 0.7 # Lower is more sensitive
SPEEDS_AROUND_PEAK_DELETION = 3 # to delete +-3mm/s around a peak
ANGLES_VALLEY_DETECTION_THRESHOLD = 1.1 # Lower is more sensitive

KLIPPAIN_COLORS = {
    "purple": "#70088C",
    "orange": "#FF8D32",
    "dark_purple": "#150140",
    "dark_orange": "#F24130",
    "red_pink": "#F2055C"
}


######################################################################
# Computation
######################################################################

# Call to the official Klipper input shaper object to do the PSD computation
def calc_freq_response(data):
    helper = shaper_calibrate.ShaperCalibrate(printer=None)
    return helper.process_accelerometer_data(data)


# Calculate motor frequency profiles based on the measured Power Spectral Density (PSD) measurements for the machine kinematics
# main angles and then create a global motor profile as a weighted average (from their own vibrations) of all calculated profiles
def compute_motor_profiles(freqs, psds, all_angles_energy, measured_angles=[0, 90], energy_amplification_factor=2):
    motor_profiles = {}
    weighted_sum_profiles = np.zeros_like(freqs)
    total_weight = 0
    conv_filter = np.ones(20) / 20

    # Creating the PSD motor profiles for each angles
    for angle in measured_angles:
        # Calculate the sum of PSDs for the current angle and then convolve
        sum_curve = np.sum(np.array([psds[angle][speed] for speed in psds[angle]]), axis=0)
        motor_profiles[angle] = np.convolve(sum_curve / len(psds[angle]), conv_filter, mode='same')

        # Calculate weights
        angle_energy = all_angles_energy[angle] ** energy_amplification_factor # First weighting factor is based on the total vibrations of the machine at the specified angle
        curve_area = np.trapz(motor_profiles[angle], freqs) ** energy_amplification_factor # Additional weighting factor is based on the area under the current motor profile at this specified angle
        total_angle_weight = angle_energy * curve_area

        # Update weighted sum profiles to get the global motor profile
        weighted_sum_profiles += motor_profiles[angle] * total_angle_weight
        total_weight += total_angle_weight

    # Creating a global average motor profile that is the weighted average of all the PSD motor profiles
    global_motor_profile = weighted_sum_profiles / total_weight if total_weight != 0 else weighted_sum_profiles

    return motor_profiles, global_motor_profile


# Since it was discovered that there is no non-linear mixing in the stepper "steps" vibrations, instead of measuring
# the effects of each speeds at each angles, this function simplify it by using only the main motors axes (X/Y for Cartesian
# printers and A/B for CoreXY) measurements and project each points on the [0,360] degrees range using trigonometry
# to "sum" the vibration impact of each axis at every points of the generated spectrogram. The result is very similar at the end.
def compute_dir_speed_spectrogram(measured_speeds, data, kinematics="cartesian", measured_angles=[0, 90]):
    # We want to project the motor vibrations measured on their own axes on the [0, 360] range
    spectrum_angles = np.linspace(0, 360, 720) # One point every 0.5 degrees
    spectrum_speeds = np.linspace(min(measured_speeds), max(measured_speeds), len(measured_speeds) * 6)
    spectrum_vibrations = np.zeros((len(spectrum_angles), len(spectrum_speeds)))

    def get_interpolated_vibrations(data, speed, speeds):
        idx = np.clip(np.searchsorted(speeds, speed, side="left"), 1, len(speeds) - 1)
        lower_speed = speeds[idx - 1]
        upper_speed = speeds[idx]
        lower_vibrations = data.get(lower_speed, 0)
        upper_vibrations = data.get(upper_speed, 0)
        return lower_vibrations + (speed - lower_speed) * (upper_vibrations - lower_vibrations) / (upper_speed - lower_speed)
    
    # Precompute trigonometric values and constant before the loop
    angle_radians = np.deg2rad(spectrum_angles)
    cos_vals = np.cos(angle_radians)
    sin_vals = np.sin(angle_radians)
    sqrt_2_inv = 1 / math.sqrt(2)

    # Compute the spectrum vibrations for each angle and speed combination
    for target_angle_idx, (cos_val, sin_val) in enumerate(zip(cos_vals, sin_vals)):
        for target_speed_idx, target_speed in enumerate(spectrum_speeds):
            if kinematics == "cartesian":
                speed_1 = np.abs(target_speed * cos_val)
                speed_2 = np.abs(target_speed * sin_val)
            elif kinematics == "corexy":
                speed_1 = np.abs(target_speed * (cos_val + sin_val) * sqrt_2_inv)
                speed_2 = np.abs(target_speed * (cos_val - sin_val) * sqrt_2_inv)

            vibrations_1 = get_interpolated_vibrations(data[measured_angles[0]], speed_1, measured_speeds)
            vibrations_2 = get_interpolated_vibrations(data[measured_angles[1]], speed_2, measured_speeds)
            spectrum_vibrations[target_angle_idx, target_speed_idx] = vibrations_1 + vibrations_2

    return spectrum_angles, spectrum_speeds, spectrum_vibrations


def compute_angle_powers(spectrogram_data):
    angles_powers = np.trapz(spectrogram_data, axis=1)

    # Since we want to plot it on a continuous polar plot later on, we need to append parts of
    # the array to start and end of it to smooth transitions when doing the convolution
    # and get the same value at modulo 360. Then we return the array without the extras
    extended_angles_powers = np.concatenate([angles_powers[-9:], angles_powers, angles_powers[:9]])
    convolved_extended = np.convolve(extended_angles_powers, np.ones(15)/15, mode='same')

    return convolved_extended[9:-9]


def compute_speed_powers(spectrogram_data, smoothing_window=15):
    min_values = np.amin(spectrogram_data, axis=0)
    max_values = np.amax(spectrogram_data, axis=0)
    var_values = np.var(spectrogram_data, axis=0)

    # rescale the variance to the same range as max_values to plot it on the same graph
    var_values = var_values / var_values.max() * max_values.max()

    # Create a vibration metric that is the product of the max values and the variance to quantify the best
    # speeds that have at the same time a low global energy level that is also consistent at every angles
    vibration_metric = max_values * var_values
    
    # utility function to pad and smooth the data avoiding edge effects
    conv_filter = np.ones(smoothing_window) / smoothing_window
    window = int(smoothing_window / 2)
    def pad_and_smooth(data):
        data_padded = np.pad(data, (window,), mode='edge')
        smoothed_data = np.convolve(data_padded, conv_filter, mode='valid')
        return smoothed_data

    # Stack the arrays and apply padding and smoothing in batch
    data_arrays = np.stack([min_values, max_values, var_values, vibration_metric])
    smoothed_arrays = np.array([pad_and_smooth(data) for data in data_arrays])

    return smoothed_arrays


# This function allow the computation of a symmetry score that reflect the spectrogram apparent symmetry between
# measured axes on both the shape of the signal and the energy level consistency across both side of the signal
def compute_symmetry_analysis(all_angles, spectrogram_data, measured_angles=[0, 90]):
    total_spectrogram_angles = len(all_angles)
    half_spectrogram_angles = total_spectrogram_angles // 2

    # Extend the spectrogram by adding half to the beginning (in order to not get an out of bounds error later)
    extended_spectrogram = np.concatenate((spectrogram_data[-half_spectrogram_angles:], spectrogram_data), axis=0)

    # Calculate the split index directly within the slicing
    midpoint_angle = np.mean(measured_angles)
    split_index = int(midpoint_angle * (total_spectrogram_angles / 360) + half_spectrogram_angles)
    half_segment_length = half_spectrogram_angles // 2

    # Slice out the two segments of the spectrogram and flatten them for comparison
    segment_1_flattened = extended_spectrogram[split_index - half_segment_length:split_index].flatten()
    segment_2_flattened = extended_spectrogram[split_index:split_index + half_segment_length].flatten()

    # Compute the correlation coefficient between the two segments of spectrogram
    correlation = np.corrcoef(segment_1_flattened, segment_2_flattened)[0, 1]
    percentage_correlation_biased = (100 * np.power(correlation, 0.75)) + 10

    return np.clip(0, 100, percentage_correlation_biased)


######################################################################
# Graphing
######################################################################

def plot_angle_profile_polar(ax, angles, angles_powers, low_energy_zones, symmetry_factor):
    angles_radians = np.deg2rad(angles)

    ax.set_title("Polar angle energy profile", fontsize=14, color=KLIPPAIN_COLORS['dark_orange'], weight='bold')
    ax.set_theta_zero_location('E')
    ax.set_theta_direction(1)

    ax.plot(angles_radians, angles_powers, color=KLIPPAIN_COLORS['purple'], zorder=5)
    ax.fill(angles_radians, angles_powers, color=KLIPPAIN_COLORS['purple'], alpha=0.3)
    ax.set_xlim([0, np.deg2rad(360)])
    ymax = angles_powers.max() * 1.05
    ax.set_ylim([0, ymax])
    ax.set_thetagrids([theta * 15 for theta in range(360//15)])

    ax.text(0, 0, f'Symmetry: {symmetry_factor:.1f}%', ha='center', va='center', color=KLIPPAIN_COLORS['red_pink'], fontsize=12, fontweight='bold', zorder=6)

    for _, (start, end, _) in enumerate(low_energy_zones):
        ax.axvline(angles_radians[start], angles_powers[start]/ymax, color=KLIPPAIN_COLORS['red_pink'], linestyle='dotted', linewidth=1.5)
        ax.axvline(angles_radians[end], angles_powers[end]/ymax, color=KLIPPAIN_COLORS['red_pink'], linestyle='dotted', linewidth=1.5)
        ax.fill_between(angles_radians[start:end], angles_powers[start:end], angles_powers.max() * 1.05, color='green', alpha=0.2)

    ax.xaxis.set_minor_locator(matplotlib.ticker.AutoMinorLocator())
    ax.yaxis.set_minor_locator(matplotlib.ticker.AutoMinorLocator())
    ax.grid(which='major', color='grey')
    ax.grid(which='minor', color='lightgrey')

    # Polar plot doesn't follow the gridspec margin, so we adjust it manually here
    pos = ax.get_position()
    new_pos = [pos.x0 - 0.01, pos.y0 - 0.01, pos.width, pos.height]
    ax.set_position(new_pos)

    return

def plot_global_speed_profile(ax, all_speeds, sp_min_energy, sp_max_energy, sp_variance_energy, vibration_metric, num_peaks, peaks, low_energy_zones):
    ax.set_title("Global speed energy profile", fontsize=14, color=KLIPPAIN_COLORS['dark_orange'], weight='bold')
    ax.set_xlabel('Speed (mm/s)')
    ax.set_ylabel('Energy')
    ax2 = ax.twinx()
    ax2.yaxis.set_visible(False)

    ax.plot(all_speeds, sp_min_energy, label='Minimum', color=KLIPPAIN_COLORS['dark_purple'], zorder=5)
    ax.plot(all_speeds, sp_max_energy, label='Maximum', color=KLIPPAIN_COLORS['purple'], zorder=5)
    ax.plot(all_speeds, sp_variance_energy, label='Variance', color=KLIPPAIN_COLORS['orange'], zorder=5, linestyle='--')
    ax2.plot(all_speeds, vibration_metric, label=f'Vibration metric ({num_peaks} bad peaks)', color=KLIPPAIN_COLORS['red_pink'], zorder=5)

    ax.set_xlim([all_speeds.min(), all_speeds.max()])
    ax.set_ylim([0, sp_max_energy.max() * 1.15])

    y2min = -(vibration_metric.max() * 0.025)
    y2max = vibration_metric.max() * 1.07
    ax2.set_ylim([y2min, y2max])

    if peaks is not None:
        ax2.plot(all_speeds[peaks], vibration_metric[peaks], "x", color='black', markersize=8, zorder=10)
        for idx, peak in enumerate(peaks):
            ax2.annotate(f"{idx+1}", (all_speeds[peak], vibration_metric[peak]),
                        textcoords="offset points", xytext=(5, 5), fontweight='bold',
                        ha='left', fontsize=13, color=KLIPPAIN_COLORS['red_pink'], zorder=10)

    for idx, (start, end, _) in enumerate(low_energy_zones):
        # ax2.axvline(all_speeds[start], color=KLIPPAIN_COLORS['red_pink'], linestyle='dotted', linewidth=1.5, zorder=8)
        # ax2.axvline(all_speeds[end], color=KLIPPAIN_COLORS['red_pink'], linestyle='dotted', linewidth=1.5, zorder=8)
        ax2.fill_between(all_speeds[start:end], y2min, vibration_metric[start:end], color='green', alpha=0.2, label=f'Zone {idx+1}: {all_speeds[start]:.1f} to {all_speeds[end]:.1f} mm/s')

    ax.xaxis.set_minor_locator(matplotlib.ticker.AutoMinorLocator())
    ax.yaxis.set_minor_locator(matplotlib.ticker.AutoMinorLocator())
    ax.grid(which='major', color='grey')
    ax.grid(which='minor', color='lightgrey')

    fontP = matplotlib.font_manager.FontProperties()
    fontP.set_size('small')
    ax.legend(loc='upper left', prop=fontP)
    ax2.legend(loc='upper right', prop=fontP)

    return

def plot_angular_speed_profiles(ax, speeds, angles, spectrogram_data, kinematics="cartesian"):
    ax.set_title("Angular speed energy profiles", fontsize=14, color=KLIPPAIN_COLORS['dark_orange'], weight='bold')
    ax.set_xlabel('Speed (mm/s)')
    ax.set_ylabel('Energy')

    # Define mappings for labels and colors to simplify plotting commands
    angle_settings = {
        0: ('X (0 deg)', 'purple', 10),
        90: ('Y (90 deg)', 'dark_purple', 5),
        45: ('A (45 deg)' if kinematics == "corexy" else '45 deg', 'orange', 10),
        135: ('B (135 deg)' if kinematics == "corexy" else '135 deg', 'dark_orange', 5),
    }

    # Plot each angle using settings from the dictionary
    for angle, (label, color, zorder) in angle_settings.items():
        idx = np.searchsorted(angles, angle, side="left")
        ax.plot(speeds, spectrogram_data[idx], label=label, color=KLIPPAIN_COLORS[color], zorder=zorder)

    ax.set_xlim([speeds.min(), speeds.max()])
    max_value = max(spectrogram_data[angle].max() for angle in [0, 45, 90, 135])
    ax.set_ylim([0, max_value * 1.1])
    
    ax.xaxis.set_minor_locator(matplotlib.ticker.AutoMinorLocator())
    ax.yaxis.set_minor_locator(matplotlib.ticker.AutoMinorLocator())
    ax.grid(which='major', color='grey')
    ax.grid(which='minor', color='lightgrey')

    fontP = matplotlib.font_manager.FontProperties()
    fontP.set_size('small')
    ax.legend(loc='upper right', prop=fontP)

    return

def plot_motor_profiles(ax, freqs, main_angles, motor_profiles, global_motor_profile, max_freq):
    ax.set_title("Motor frequency profile", fontsize=14, color=KLIPPAIN_COLORS['dark_orange'], weight='bold')
    ax.set_ylabel('Energy')
    ax.set_xlabel('Frequency (Hz)')

    ax2 = ax.twinx()
    ax2.yaxis.set_visible(False)

    # Global weighted average motor profile
    ax.plot(freqs, global_motor_profile, label="Combined", color=KLIPPAIN_COLORS['purple'], zorder=5)
    max_value = global_motor_profile.max()

    # Mapping of angles to axis names
    angle_settings = {
        0: "X",
        90: "Y",
        45: "A",
        135: "B"
    }

    # And then plot the motor profiles at each measured angles
    for angle in main_angles:
        profile_max = motor_profiles[angle].max()
        if profile_max > max_value:
            max_value = profile_max
        label = f"{angle_settings[angle]} ({angle} deg)" if angle in angle_settings else f"{angle} deg"
        ax.plot(freqs, motor_profiles[angle], linestyle='--', label=label, zorder=2)

    ax.set_xlim([0, max_freq])
    ax.set_ylim([0, max_value * 1.1])
    ax.ticklabel_format(axis='y', style='scientific', scilimits=(0,0))

    # Then add the motor resonance peak to the graph and print some infos about it
    motor_fr, motor_zeta, motor_res_idx, lowfreq_max = compute_mechanical_parameters(global_motor_profile, freqs, 30)
    if lowfreq_max:
        print_with_c_locale("[WARNING] There are a lot of low frequency vibrations that can alter the readings. This is probably due to the test being performed at too high an acceleration!")
        print_with_c_locale("Try lowering the ACCEL value and/or increasing the SIZE value before restarting the macro to ensure that only constant speeds are being recorded and that the dynamic behavior of the machine is not affecting the measurements")
    if motor_zeta is not None:
        print_with_c_locale("Motors have a main resonant frequency at %.1fHz with an estimated damping ratio of %.3f" % (motor_fr, motor_zeta))
    else:
        print_with_c_locale("Motors have a main resonant frequency at %.1fHz but it was impossible to estimate a damping ratio." % (motor_fr))

    ax.plot(freqs[motor_res_idx], global_motor_profile[motor_res_idx], "x", color='black', markersize=10)
    ax.annotate(f"R", (freqs[motor_res_idx], global_motor_profile[motor_res_idx]),
                textcoords="offset points", xytext=(15, 5),
                ha='right', fontsize=14, color=KLIPPAIN_COLORS['red_pink'], weight='bold')

    ax2.plot([], [], ' ', label="Motor resonant frequency (ω0): %.1fHz" % (motor_fr))
    if motor_zeta is not None:
        ax2.plot([], [], ' ', label="Motor damping ratio (ζ): %.3f" % (motor_zeta))
    else:
        ax2.plot([], [], ' ', label="No damping ratio computed")

    ax.xaxis.set_minor_locator(matplotlib.ticker.AutoMinorLocator())
    ax.yaxis.set_minor_locator(matplotlib.ticker.AutoMinorLocator())
    ax.grid(which='major', color='grey')
    ax.grid(which='minor', color='lightgrey')

    fontP = matplotlib.font_manager.FontProperties()
    fontP.set_size('small')
    ax.legend(loc='upper left', prop=fontP)
    ax2.legend(loc='upper right', prop=fontP)

    return

def plot_vibration_spectrogram_polar(ax, angles, speeds, spectrogram_data):
    angles_radians = np.radians(angles)

    # Assuming speeds defines the radial distance from the center, we need to create a meshgrid
    # for both angles and speeds to map the spectrogram data onto a polar plot correctly
    radius, theta = np.meshgrid(speeds, angles_radians)

    ax.set_title("Polar vibrations heatmap", fontsize=14, color=KLIPPAIN_COLORS['dark_orange'], weight='bold', va='bottom')
    ax.set_theta_zero_location("E")
    ax.set_theta_direction(1)

    ax.pcolormesh(theta, radius, spectrogram_data, norm=matplotlib.colors.LogNorm(), cmap='inferno', shading='auto')
    ax.set_thetagrids([theta * 15 for theta in range(360//15)])
    ax.tick_params(axis='y', which='both', colors='white', labelsize='medium')
    ax.set_ylim([0, max(speeds)])

    # Polar plot doesn't follow the gridspec margin, so we adjust it manually here
    pos = ax.get_position()
    new_pos = [pos.x0 - 0.01, pos.y0 - 0.01, pos.width, pos.height]
    ax.set_position(new_pos)

    return

def plot_vibration_spectrogram(ax, angles, speeds, spectrogram_data, peaks):
    ax.set_title("Vibrations heatmap", fontsize=14, color=KLIPPAIN_COLORS['dark_orange'], weight='bold')
    ax.set_xlabel('Speed (mm/s)')
    ax.set_ylabel('Angle (deg)')

    ax.imshow(spectrogram_data, norm=matplotlib.colors.LogNorm(), cmap='inferno',
              aspect='auto', extent=[speeds[0], speeds[-1], angles[0], angles[-1]],
              origin='lower', interpolation='antialiased')
    
    # Add peaks lines in the spectrogram to get hint from peaks found in the first graph
    if peaks is not None:
        for idx, peak in enumerate(peaks):
            ax.axvline(speeds[peak], color='cyan', linewidth=0.75)
            ax.annotate(f"Peak {idx+1}", (speeds[peak], angles[-1]*0.9),
                        textcoords="data", color='cyan', rotation=90, fontsize=10,
                        verticalalignment='top', horizontalalignment='right')

    return


######################################################################
# Startup and main routines
######################################################################

def extract_angle_and_speed(logname):
    try:
        match = re.search(r'an(\d+)_\d+sp(\d+)_\d+', os.path.basename(logname))
        if match:
            angle = match.group(1)
            speed = match.group(2)
    except AttributeError:
        raise ValueError(f"File {logname} does not match expected format.")
    return float(angle), float(speed)


def vibrations_profile(lognames, klipperdir="~/klipper", kinematics="cartesian", accel=None, max_freq=1000.):
    set_locale()
    global shaper_calibrate
    shaper_calibrate = setup_klipper_import(klipperdir)

    if kinematics == "cartesian": main_angles = [0, 90]
    elif kinematics == "corexy": main_angles = [45, 135]
    else:
        raise ValueError("Only Cartesian and CoreXY kinematics are supported by this tool at the moment!")

    psds = defaultdict(lambda: defaultdict(list))
    psds_sum = defaultdict(lambda: defaultdict(list))
    target_freqs_initialized = False

    for logname in lognames:
        data = parse_log(logname)
        angle, speed = extract_angle_and_speed(logname)
        freq_response = calc_freq_response(data)
        first_freqs = freq_response.freq_bins
        psd_sum = freq_response.psd_sum

        if not target_freqs_initialized:
            target_freqs = first_freqs[first_freqs <= max_freq]
            target_freqs_initialized = True
        
        psd_sum = psd_sum[first_freqs <= max_freq]
        first_freqs = first_freqs[first_freqs <= max_freq]

        # Store the interpolated PSD and integral values
        psds[angle][speed] = np.interp(target_freqs, first_freqs, psd_sum)
        psds_sum[angle][speed] = np.trapz(psd_sum, first_freqs)

    measured_angles = sorted(psds_sum.keys())
    measured_speeds = sorted({speed for angle_speeds in psds_sum.values() for speed in angle_speeds.keys()})

    for main_angle in main_angles:
        if main_angle not in measured_angles:
            raise ValueError("Measurements not taken at the correct angles for the specified kinematics!")

    # Precompute the variables used in plot functions
    all_angles, all_speeds, spectrogram_data = compute_dir_speed_spectrogram(measured_speeds, psds_sum, kinematics, main_angles)
    all_angles_energy = compute_angle_powers(spectrogram_data)
    sp_min_energy, sp_max_energy, sp_variance_energy, vibration_metric = compute_speed_powers(spectrogram_data)
    motor_profiles, global_motor_profile = compute_motor_profiles(target_freqs, psds, all_angles_energy, main_angles)

    # symmetry_factor = compute_symmetry_analysis(all_angles, all_angles_energy)
    symmetry_factor = compute_symmetry_analysis(all_angles, spectrogram_data, main_angles)
    print_with_c_locale(f"Machine estimated vibration symmetry: {symmetry_factor:.1f}%")

    # Analyze low variance ranges of vibration energy across all angles for each speed to identify clean speeds
    # and highlight them. Also find the peaks to identify speeds to avoid due to high resonances
    num_peaks, vibration_peaks, peaks_speeds = detect_peaks(
        vibration_metric, all_speeds,
        PEAKS_DETECTION_THRESHOLD * vibration_metric.max(),
        PEAKS_RELATIVE_HEIGHT_THRESHOLD, 10, 10
        )
    formated_peaks_speeds = ["{:.1f}".format(pspeed) for pspeed in peaks_speeds]
    print_with_c_locale("Vibrations peaks detected: %d @ %s mm/s (avoid setting a speed near these values in your slicer print profile)" % (num_peaks, ", ".join(map(str, formated_peaks_speeds))))
    
    good_speeds = identify_low_energy_zones(vibration_metric, SPEEDS_VALLEY_DETECTION_THRESHOLD)
    if good_speeds is not None:
        deletion_range = int(SPEEDS_AROUND_PEAK_DELETION / (all_speeds[1] - all_speeds[0]))
        peak_speed_indices = {pspeed: np.where(all_speeds == pspeed)[0][0] for pspeed in set(peaks_speeds)}

        filtered_good_speeds = []
        for start, end, energy in good_speeds:
            # Check for peaks within the current good speed range
            start_speed, end_speed = all_speeds[start], all_speeds[end]
            intersecting_peaks_indices = [idx for speed, idx in peak_speed_indices.items() if start_speed <= speed <= end_speed]

            # If no peaks intersect any good_speed range, add it as is, else iterate through intersecting peaks to split the range
            if not intersecting_peaks_indices: filtered_good_speeds.append((start, end, energy))
            else:
                for peak_index in intersecting_peaks_indices:
                    before_peak_end = max(start, peak_index - deletion_range)
                    after_peak_start = min(end, peak_index + deletion_range)
                    if start < before_peak_end:
                        filtered_good_speeds.append((start, before_peak_end, energy))
                    if after_peak_start < end:
                        filtered_good_speeds.append((after_peak_start, end, energy))

        good_speeds = filtered_good_speeds
        print_with_c_locale(f'Lowest vibrations speeds ({len(good_speeds)} ranges sorted from best to worse):')
        for idx, (start, end, energy) in enumerate(good_speeds):
            print_with_c_locale(f'{idx+1}: {all_speeds[start]:.1f} to {all_speeds[end]:.1f} mm/s')

    # Angle low energy valleys identification (good angles ranges) and print them to the console
    good_angles = identify_low_energy_zones(all_angles_energy, ANGLES_VALLEY_DETECTION_THRESHOLD)
    if good_angles is not None:
        print_with_c_locale(f'Lowest vibrations angles ({len(good_angles)} ranges sorted from best to worse):')
        for idx, (start, end, energy) in enumerate(good_angles):
            print_with_c_locale(f'{idx+1}: {all_angles[start]:.1f}° to {all_angles[end]:.1f}° (mean vibrations energy: {energy:.2f}% of max)')

    # Create graph layout
    fig, ((ax1, ax2, ax3), (ax4, ax5, ax6)) = plt.subplots(2, 3, gridspec_kw={
            'height_ratios':[1, 1],
            'width_ratios':[4, 8, 6],
            'bottom':0.050,
            'top':0.890,
            'left':0.040,
            'right':0.985,
            'hspace':0.166,
            'wspace':0.138
            })

    # Transform ax3 and ax4 to polar plots
    ax1.remove()
    ax1 = fig.add_subplot(2, 3, 1, projection='polar')
    ax4.remove()
    ax4 = fig.add_subplot(2, 3, 4, projection='polar')

    # Set the global .png figure size
    fig.set_size_inches(20, 11.5)

    # Add title
    title_line1 = "MACHINE VIBRATIONS ANALYSIS TOOL"
    fig.text(0.060, 0.965, title_line1, ha='left', va='bottom', fontsize=20, color=KLIPPAIN_COLORS['purple'], weight='bold')
    try:
        filename_parts = (lognames[0].split('/')[-1]).split('_')
        dt = datetime.strptime(f"{filename_parts[1]} {filename_parts[2].split('-')[0]}", "%Y%m%d %H%M%S")
        title_line2 = dt.strftime('%x %X')
        if accel is not None:
            title_line2 += ' at ' + str(accel) + ' mm/s² -- ' + kinematics.upper() + ' kinematics'
    except:
        print_with_c_locale("Warning: CSV filenames appear to be different than expected (%s)" % (lognames[0]))
        title_line2 = lognames[0].split('/')[-1]
    fig.text(0.060, 0.957, title_line2, ha='left', va='top', fontsize=16, color=KLIPPAIN_COLORS['dark_purple'])

    # Plot the graphs
    plot_angle_profile_polar(ax1, all_angles, all_angles_energy, good_angles, symmetry_factor)
    plot_vibration_spectrogram_polar(ax4, all_angles, all_speeds, spectrogram_data)

    plot_global_speed_profile(ax2, all_speeds, sp_min_energy, sp_max_energy, sp_variance_energy, vibration_metric, num_peaks, vibration_peaks, good_speeds)
    plot_angular_speed_profiles(ax3, all_speeds, all_angles, spectrogram_data, kinematics)
    plot_vibration_spectrogram(ax5, all_angles, all_speeds, spectrogram_data, vibration_peaks)

    plot_motor_profiles(ax6, target_freqs, main_angles, motor_profiles, global_motor_profile, max_freq)

    # Adding a small Klippain logo to the top left corner of the figure
    ax_logo = fig.add_axes([0.001, 0.924, 0.075, 0.075], anchor='NW')
    ax_logo.imshow(plt.imread(os.path.join(os.path.dirname(os.path.abspath(__file__)), 'klippain.png')))
    ax_logo.axis('off')

    # Adding Shake&Tune version in the top right corner
    st_version = get_git_version()
    if st_version is not None:
        fig.text(0.995, 0.985, st_version, ha='right', va='bottom', fontsize=8, color=KLIPPAIN_COLORS['purple'])

    return fig


def main():
    # Parse command-line arguments
    usage = "%prog [options] <raw logs>"
    opts = optparse.OptionParser(usage)
    opts.add_option("-o", "--output", type="string", dest="output",
                    default=None, help="filename of output graph")
    opts.add_option("-c", "--accel", type="int", dest="accel",
                    default=None, help="accel value to be printed on the graph")
    opts.add_option("-f", "--max_freq", type="float", default=1000.,
                    help="maximum frequency to graph")
    opts.add_option("-k", "--klipper_dir", type="string", dest="klipperdir",
                    default="~/klipper", help="main klipper directory")
    opts.add_option("-m", "--kinematics", type="string", dest="kinematics",
                    default="cartesian", help="machine kinematics configuration")
    options, args = opts.parse_args()
    if len(args) < 1:
        opts.error("No CSV file(s) to analyse")
    if options.output is None:
        opts.error("You must specify an output file.png to use the script (option -o)")
    if options.kinematics not in ["cartesian", "corexy"]:
        opts.error("Only cartesian and corexy kinematics are supported by this tool at the moment!")

    fig = vibrations_profile(args, options.klipperdir, options.kinematics, options.accel, options.max_freq)
    fig.savefig(options.output, dpi=150)


if __name__ == '__main__':
    main()