A rainflow counting matrix visualizes the results of rainflow cycle counting from a load or stress time history. The matrix displays cycle counts as a 2D heatmap where one axis represents cycle amplitude (half-range), the other represents cycle mean value, and color intensity represents the frequency of each cycle combination. This is a fundamental tool in fatigue analysis and durability engineering, used to characterize variable-amplitude loading for fatigue life prediction.
""" anyplot.ai
heatmap-rainflow: Rainflow Counting Matrix for Fatigue Analysis
Library: plotly 6.7.0 | Python 3.13.13
Quality: 90/100 | Updated: 2026-06-02
"""
import os
import numpy as np
import plotly.graph_objects as go
# Theme tokens — Imprint palette chrome
THEME = os.getenv("ANYPLOT_THEME", "light")
PAGE_BG = "#FAF8F1" if THEME == "light" else "#1A1A17"
ELEVATED_BG = "#FFFDF6" if THEME == "light" else "#242420"
INK = "#1A1A17" if THEME == "light" else "#F0EFE8"
INK_SOFT = "#4A4A44" if THEME == "light" else "#B8B7B0"
INK_MUTED = "#6B6A63" if THEME == "light" else "#A8A79F"
GRID = "rgba(26,26,23,0.15)" if THEME == "light" else "rgba(240,239,232,0.15)"
# Imprint sequential colormap for single-polarity cycle count data
imprint_seq = [[0.0, "#009E73"], [1.0, "#4467A3"]]
# Data — rainflow matrix: exponential decay in amplitude × Gaussian in mean stress
# Physically realistic: most cycles are small (exponential amplitude distribution),
# centred around service mean stress with a tensile-dominated secondary regime.
np.random.seed(42)
n_bins = 20
amplitude_edges = np.linspace(10, 200, n_bins + 1)
mean_edges = np.linspace(-50, 250, n_bins + 1)
amplitude_centers = (amplitude_edges[:-1] + amplitude_edges[1:]) / 2
mean_centers = (mean_edges[:-1] + mean_edges[1:]) / 2
amp_grid, mean_grid = np.meshgrid(amplitude_centers, mean_centers, indexing="ij")
# Exponential amplitude decay (characteristic amplitude ~45 MPa)
amp_decay = np.exp(-amp_grid / 45)
# Primary cluster: baseline service loads, mean ~100 MPa
mean_primary = np.exp(-((mean_grid - 100) ** 2) / (2 * 55**2))
counts = 850 * amp_decay * mean_primary
# Secondary cluster: tensile-dominated regime, mean ~175 MPa
mean_secondary = np.exp(-((mean_grid - 175) ** 2) / (2 * 25**2))
counts += 180 * amp_decay * mean_secondary
# Poisson-like scatter noise
counts += np.random.exponential(1.5, counts.shape)
counts = np.round(counts).astype(int)
counts = np.clip(counts, 0, None)
counts[counts < 2] = 0
# NaN for zero-count bins → transparent (PAGE_BG shows through)
z_display = counts.astype(float)
z_display[z_display == 0] = np.nan
# Sqrt-transform for perceptual range enhancement — the 2-600 linear span makes
# moderate bins indistinguishable; sqrt(2)≈1.4 → sqrt(600)≈24.5 spreads them well.
z_max = int(np.nanmax(z_display))
z_plot = np.sqrt(z_display)
# Colorbar ticks: sqrt-transformed positions labeled with original counts
raw_ticks = [v for v in [2, 25, 100, 200, 400, z_max] if v <= z_max]
cb_tickvals = [np.sqrt(v) for v in raw_ticks]
cb_ticktext = [str(v) for v in raw_ticks]
font_family = "Palatino, Georgia, serif"
title_text = "heatmap-rainflow · python · plotly · anyplot.ai"
n_chars = len(title_text)
ratio = 67 / n_chars if n_chars > 67 else 1.0
title_size = max(11, round(16 * ratio))
# Plot
fig = go.Figure(
data=go.Heatmap(
z=z_plot,
x=np.round(mean_centers, 1),
y=np.round(amplitude_centers, 1),
colorscale=imprint_seq,
colorbar={
"title": {"text": "Cycle Count", "font": {"size": 12, "family": font_family, "color": INK}},
"tickfont": {"size": 10, "family": font_family, "color": INK_SOFT},
"tickvals": cb_tickvals,
"ticktext": cb_ticktext,
"thickness": 18,
"len": 0.75,
"outlinewidth": 0,
"bgcolor": ELEVATED_BG,
},
hovertemplate="Mean: %{x} MPa<br>Amplitude: %{y} MPa<br>Cycles: %{customdata:.0f}<extra></extra>",
customdata=z_display,
xgap=1,
ygap=1,
connectgaps=False,
)
)
# Annotations — absolute data-coordinate placement (axref/ayref="x"/"y") keeps
# text boxes inside the plot regardless of pixel scaling.
fig.add_annotation(
xref="x",
yref="y",
axref="x",
ayref="y",
x=100,
y=25,
ax=5,
ay=148,
text="<b>Primary service loads</b><br>Low-amplitude cycles<br>dominate count",
showarrow=True,
arrowhead=2,
arrowsize=1.2,
arrowwidth=2,
arrowcolor=INK_SOFT,
font={"size": 13, "family": font_family, "color": INK},
bgcolor=ELEVATED_BG,
bordercolor=INK_SOFT,
borderpad=5,
borderwidth=1,
)
fig.add_annotation(
xref="x",
yref="y",
axref="x",
ayref="y",
x=175,
y=20,
ax=110,
ay=120,
text="<b>Tensile-dominated</b><br>loading regime",
showarrow=True,
arrowhead=2,
arrowsize=1.2,
arrowwidth=2,
arrowcolor=INK_MUTED,
font={"size": 13, "family": font_family, "color": INK_MUTED},
bgcolor=ELEVATED_BG,
bordercolor=INK_SOFT,
borderpad=4,
borderwidth=1,
)
fig.update_layout(
autosize=False,
title={
"text": title_text,
"font": {"size": title_size, "family": font_family, "color": INK},
"x": 0.5,
"xanchor": "center",
},
xaxis={
"title": {"text": "Cycle Mean Stress (MPa)", "font": {"size": 12, "family": font_family, "color": INK}},
"tickfont": {"size": 10, "family": font_family, "color": INK_SOFT},
"gridcolor": GRID,
"linecolor": INK_SOFT,
"zerolinecolor": INK_SOFT,
},
yaxis={
"title": {"text": "Cycle Amplitude (MPa)", "font": {"size": 12, "family": font_family, "color": INK}},
"tickfont": {"size": 10, "family": font_family, "color": INK_SOFT},
"gridcolor": GRID,
"linecolor": INK_SOFT,
"zerolinecolor": INK_SOFT,
"range": [5, 205],
},
paper_bgcolor=PAGE_BG,
plot_bgcolor=PAGE_BG,
font={"color": INK},
margin={"l": 80, "r": 60, "t": 80, "b": 60},
)
# Save — square canvas (2400×2400) suits the symmetric heatmap grid
fig.write_image(f"plot-{THEME}.png", width=600, height=600, scale=4)
fig.write_html(f"plot-{THEME}.html", include_plotlyjs="cdn")
Part of Rainflow Counting Matrix for Fatigue Analysis on anyplot.ai.