generate_dataset.py

"""
IPA Roller Compaction Synthetic Dataset Generator v1.0
========================================================
Generates a physically plausible synthetic dataset based on:
  - Johanson rolling theory (Johanson, 1965) for nip angle & pressure
  - Heckel equation for powder densification under pressure
  - Empirical twin-feed-screw effect on ribbon uniformity

THIS IS SYNTHETIC EDUCATIONAL DATA. NOT REAL CUSTOMER OR LAB DATA.
Generated by Innovative Process Applications (IPA) for teaching DOE/RSM.
"""

import numpy as np
import pandas as pd

rng = np.random.default_rng(seed=42)  # reproducible

# ---- Physical constants & realistic ranges ----
# Grounded in published roller compaction literature for pharma excipients
# (microcrystalline cellulose / lactose blends on lab-to-pilot scale rolls)

N_RUNS = 600  # enough for DOE/RSM teaching, small enough to inspect by eye

# Process parameter ranges (realistic for IPA CL-series lab/pilot compactors)
ROLL_FORCE_KN_CM = (2.0, 14.0)     # kN/cm of roll width
ROLL_SPEED_RPM   = (1.0, 12.0)     # roll rotation speed
FEED_SCREW_RPM   = (10.0, 120.0)   # twin feed screw speed
ROLL_GAP_MM      = (1.5, 4.5)      # ribbon thickness target

# Material parameters (MCC-lactose blend, representative)
RHO_TRUE = 1.55           # true density, g/cc
RHO_BULK = 0.45           # tapped bulk density, g/cc
HECKEL_K = 0.018          # 1/MPa, Heckel compressibility constant
HECKEL_A = 0.62           # Heckel intercept (related to initial packing)

# Machine geometry (representative of CL2x6 class roller compactor)
ROLL_DIAMETER_MM = 150.0
ROLL_WIDTH_MM    = 50.0

def johanson_pressure_mpa(force_kn_per_cm, gap_mm):
    """
    Approximation of peak nip pressure from Johanson rolling theory.
    Pressure scales with force/(contact area), and contact area grows
    with sqrt(R * (gap_entry - gap)).
    """
    # Effective contact length proxy (mm): sqrt(R * delta_gap)
    # Assume entry gap ~ 3x exit gap for MCC-like materials
    contact_len_mm = np.sqrt(ROLL_DIAMETER_MM/2 * 2.0 * gap_mm)
    # Force per unit area: (kN/cm * 10 N/mm) / (contact_len_mm) -> MPa-ish
    pressure = (force_kn_per_cm * 100.0) / contact_len_mm
    return pressure  # MPa

def heckel_relative_density(pressure_mpa):
    """Heckel equation: ln(1/(1-D)) = K*P + A  =>  D = 1 - exp(-(K*P + A))"""
    return 1.0 - np.exp(-(HECKEL_K * pressure_mpa + HECKEL_A))

def feed_ratio_effect(feed_rpm, roll_rpm):
    """
    Twin feed screw effect: under-feeding starves the nip (low density,
    high variability); over-feeding causes slip and pre-compaction.
    Optimal ratio roughly 8-15 for twin screws on MCC.
    """
    ratio = feed_rpm / roll_rpm
    # Gaussian-like response centered at ratio=11
    optimality = np.exp(-((ratio - 11.0) ** 2) / (2 * 6.0**2))
    return optimality  # 0..1

# ---- Generate runs ----
roll_force = rng.uniform(*ROLL_FORCE_KN_CM, N_RUNS)
roll_speed = rng.uniform(*ROLL_SPEED_RPM, N_RUNS)
feed_speed = rng.uniform(*FEED_SCREW_RPM, N_RUNS)
roll_gap   = rng.uniform(*ROLL_GAP_MM, N_RUNS)

# Physics
peak_pressure = johanson_pressure_mpa(roll_force, roll_gap)
base_rel_density = heckel_relative_density(peak_pressure)
feed_opt = feed_ratio_effect(feed_speed, roll_speed)

# Combine: good feed ratio lets you reach base density; poor ratio penalizes
relative_density = base_rel_density * (0.85 + 0.15 * feed_opt)
# Add realistic measurement noise (~1.5% relative)
relative_density += rng.normal(0, 0.015, N_RUNS)
relative_density = np.clip(relative_density, 0.40, 0.95)

ribbon_density = relative_density * RHO_TRUE               # g/cc
porosity = 1.0 - relative_density                          # fraction

# Ribbon uniformity: twin feed screws give lower CV across roll width
# when feed ratio is in the sweet spot; degrades otherwise
density_cv_pct = (2.0 + 4.5 * (1 - feed_opt)) + rng.normal(0, 0.4, N_RUNS)
density_cv_pct = np.clip(density_cv_pct, 1.0, 10.0)

throughput_kg_hr = (
    roll_speed * roll_gap * ROLL_WIDTH_MM * ribbon_density * 60 / 1000 * 0.85
) + rng.normal(0, 1.5, N_RUNS)
throughput_kg_hr = np.clip(throughput_kg_hr, 0, None)

df = pd.DataFrame({
    "run_id": np.arange(1, N_RUNS + 1),
    "roll_force_kN_per_cm": np.round(roll_force, 2),
    "roll_speed_rpm": np.round(roll_speed, 2),
    "feed_screw_rpm": np.round(feed_speed, 1),
    "roll_gap_mm": np.round(roll_gap, 2),
    "peak_pressure_MPa": np.round(peak_pressure, 1),
    "ribbon_rel_density": np.round(relative_density, 4),
    "ribbon_density_g_cc": np.round(ribbon_density, 4),
    "ribbon_porosity": np.round(porosity, 4),
    "density_CV_percent": np.round(density_cv_pct, 2),
    "throughput_kg_hr": np.round(throughput_kg_hr, 2),
})

df.to_csv("ribbon_density_v1.0.csv", index=False)
print(f"Wrote {len(df)} rows")
print(df.describe().round(3))