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scheduling_rl.py β PPO-based replacement scheduling for the HP Metal Jet S100.
Environment
-----------
State : [h(9), X_t(9), budget_remaining/W(1), t_hours(1)] β R^20
Action : Discrete(512) β one of 2^9 joint component-replacement combinations
Reward : +1.0 per survived hour (dt=1); 0.0 on the terminal step
Done : any h_i < HEALTH_THRESHOLD OR replacement cost exceeds budget
Algorithm
---------
PPO (Stable-Baselines3) with a 512-output Softmax actor.
The Softmax over the full 2^9 action space captures all joint replacement
correlations without requiring an autoregressive architecture.
Actor: Linear(20β64) β Tanh β Linear(64β64) β Tanh β Linear(64β512)
Critic: Linear(20β64) β Tanh β Linear(64β64) β Tanh β Linear(64β1)
SB3 default orthogonal init + 0.01 final-layer scale β initial policy
is near-uniform over all 512 actions (max-entropy start).
Component costs (β¬)
--------------------
Sourced from analogous industrial parts; HP does not publish official prices.
Sources listed in DEFAULT_COSTS docstring below.
"""
from __future__ import annotations
import numpy as np
import torch as th
import gymnasium as gym
from gymnasium import spaces
from stable_baselines3 import PPO
from model import DegradationModel
# ---------------------------------------------------------------------------
# Constants
# ---------------------------------------------------------------------------
COMPONENT_NAMES: list[str] = [
"recoater_blade", # 0
"nozzle_plate", # 1
"heating_elements", # 2
"temperature_sensors", # 3
"insulation_panels", # 4
"firing_resistors", # 5
"cleaning_interface", # 6
"recoater_motor", # 7
"linear_rail", # 8
]
# Replacement costs in euros per component.
# Sources:
# recoater_blade β WINK3D EOS M290 ceramic blade ~$160, scaled to HP Metal Jet tier
# https://winking3d.com/product/ceramic-recoater-blade-3/
# nozzle_plate β 6Γ HP TIJ printheads; HP industrial OEM pricing estimate
# https://3dprintingindustry.com/news/hp-launches-new-metal-jet-s100...
# heating_elements β Industrial resistive heating elements for 180Β°C chamber
# https://www.sentrotech.com/heating-elements/
# temperature_sensors β Industrial PT100/thermocouple bundle (Omega, multiple sensors)
# https://www.omega.co.uk/pptst/T3PROBES.html
# insulation_panels β Ceramic fibre panel section for printer-sized chamber
# https://www.sentrotech.com/ceramic-fiber-insulation/
# firing_resistors β Printhead array embedded resistors, proprietary HP part
# cleaning_interface β Wiper blade + solvent delivery module
# https://digiprint-usa.com/blogs/printhead-guides-tips-digiprint-usa/...
# recoater_motor β 500 Wβ1 kW industrial servo motor
# https://teknic.com/products/clearpath-brushless-dc-servo-motors/
# linear_rail β THK/HIWIN precision guide rail assembly
DEFAULT_COSTS = np.array([
350.0, # recoater_blade
2500.0, # nozzle_plate
1500.0, # heating_elements
200.0, # temperature_sensors
800.0, # insulation_panels
400.0, # firing_resistors
600.0, # cleaning_interface
900.0, # recoater_motor
600.0, # linear_rail
], dtype=np.float64)
HEALTH_THRESHOLD: float = 0.1 # printer fails when any component drops below this
N_COMPONENTS: int = 9
N_ACTIONS: int = 2 ** N_COMPONENTS # 512
# Precompute action β binary replacement vector table once at import time.
# _ACTION_TABLE[i] is a (9,) float32 array: bit j = 1 means replace component j.
_ACTION_TABLE: np.ndarray = np.array(
[[int(b) for b in format(i, f"0{N_COMPONENTS}b")] for i in range(N_ACTIONS)],
dtype=np.float32,
)
# ---------------------------------------------------------------------------
# Environment
# ---------------------------------------------------------------------------
class PrinterEnv(gym.Env):
"""
Gymnasium environment wrapping DegradationModel for replacement scheduling.
Parameters
----------
model : Fitted DegradationModel with N=9 components and C inputs.
X_series : (T_max, C) array of predicted operating-condition vectors,
one row per simulated hour. If the episode outlasts X_series
the last row is repeated.
W : Total budget in euros available for the episode.
costs : (9,) replacement cost per component in euros.
Defaults to DEFAULT_COSTS when None.
dt : Simulation time-step in hours (default 1.0).
stochastic : Include Poisson shock terms from model.lambda_rates (default True).
seed : RNG seed for reproducibility.
"""
metadata: dict = {"render_modes": []}
def __init__(
self,
model: DegradationModel,
X_series: np.ndarray,
W: float,
costs: np.ndarray | None = None,
dt: float = 1.0,
stochastic: bool = True,
seed: int | None = None,
) -> None:
"""
Initialise the environment and validate inputs.
Builds the observation and action spaces, stores a reference to the
fitted DegradationModel, and sets the episode state to its initial
values (all components fully healthy, full budget, t=0).
Raises ValueError if model.N != 9.
"""
super().__init__()
if model.N != N_COMPONENTS:
raise ValueError(f"DegradationModel must have N={N_COMPONENTS}, got {model.N}")
self.model = model
self.X_series = np.asarray(X_series, dtype=np.float64) # (T_max, C)
self.W = float(W)
self.costs = (
np.asarray(costs, dtype=np.float64) if costs is not None else DEFAULT_COSTS
)
self.dt = float(dt)
self.stochastic = stochastic
self._rng = np.random.default_rng(seed)
# Observation: h(9) + X_t(C) + budget/W(1) + t_hours(1)
obs_dim = N_COMPONENTS + model.C + 2
self.observation_space = spaces.Box(
low=-np.inf, high=np.inf, shape=(obs_dim,), dtype=np.float32
)
self.action_space = spaces.Discrete(N_ACTIONS)
# Episode state β initialised properly in reset()
self._h = np.ones(N_COMPONENTS, dtype=np.float64)
self._t: float = 0.0
self._budget: float = self.W
self._step_idx: int = 0
# ------------------------------------------------------------------
# Core Gymnasium interface
# ------------------------------------------------------------------
def reset(
self,
*,
seed: int | None = None,
options: dict | None = None,
) -> tuple[np.ndarray, dict]:
"""
Reset the environment to the start of a new episode.
All components are restored to full health (h=1), the budget is
refilled to W, and the simulation clock is set to t=0. If a seed
is supplied the internal RNG is re-seeded for reproducibility.
Returns
-------
obs : (obs_dim,) float32 observation vector.
info : empty dict (required by the Gymnasium API).
"""
if seed is not None:
self._rng = np.random.default_rng(seed)
self._h = np.ones(N_COMPONENTS, dtype=np.float64)
self._t = 0.0
self._budget = self.W
self._step_idx = 0
return self._obs(), {}
def step(
self, action: int
) -> tuple[np.ndarray, float, bool, bool, dict]:
"""
Advance the simulation by one hour and apply the chosen replacements.
The action integer is decoded to a 9-bit binary replacement vector via
_ACTION_TABLE. Components whose bit is 1 are replaced (health reset to
1.0) before the ODE step is taken, so new components benefit from the
full degradation rate of a healthy part.
Budget is checked before applying replacements. If the total cost of
the selected action exceeds the remaining budget the episode terminates
immediately with reward 0 and no state change.
After replacements the health vector is updated with one Euler step:
h_{t+1} = h_t + f(h_t, X_t) * dt [- Q * H if stochastic]
where Q ~ N(0,1)Β² and H ~ Poisson(Ξ»_i * dt) are independent per
component (matching the stochastic extension in model.py Β§5).
Parameters
----------
action : int in [0, 511].
Returns
-------
obs : (obs_dim,) float32 observation after the step.
reward : dt (1.0) if the printer survived; 0.0 on failure.
terminated : True when any h_i < HEALTH_THRESHOLD or budget exceeded.
truncated : always False (no fixed time limit).
info : dict with keys t_hours, budget_remaining, min_health
(or termination on budget failure).
"""
bits = _ACTION_TABLE[int(action)] # (9,) float32 binary vector
replacement_cost = float(np.dot(bits, self.costs))
# Hard budget constraint: action is unaffordable β episode ends
if replacement_cost > self._budget:
return self._obs(), 0.0, True, False, {
"termination": "budget_exceeded",
"t_hours": self._t,
"budget_remaining": self._budget,
}
# Apply replacements: reset selected components to full health
self._budget -= replacement_cost
self._h[bits.astype(bool)] = 1.0
# Euler step: dh = f(h, X_t) * dt [+ optional stochastic shock]
X_t = self._current_X()
dh = self.model.f(self._h, X_t) * self.dt
if self.stochastic:
Q = self._rng.standard_normal(N_COMPONENTS) ** 2 # N(0,1)Β² β event intensity
H = self._rng.poisson(self.model.lambda_rates * self.dt) # Poisson(Ξ»_i Β· dt)
dh -= Q * H
self._h = self._h + dh
self._t += self.dt
self._step_idx += 1
# Failure: any component below threshold
failed = bool(np.any(self._h < HEALTH_THRESHOLD))
reward = 0.0 if failed else self.dt
return self._obs(), reward, failed, False, {
"t_hours": self._t,
"budget_remaining": self._budget,
"min_health": float(self._h.min()),
}
# ------------------------------------------------------------------
# Helpers
# ------------------------------------------------------------------
def _obs(self) -> np.ndarray:
"""
Build the current observation vector.
Layout (obs_dim = 9 + C + 2):
h[0:9] β component health values (float, may be negative
after a stochastic shock representing catastrophic
failure before the done flag is raised)
X_t[9:9+C] β current operating-condition inputs from X_series
budget/W [9+C] β remaining budget as a fraction of the initial
budget W; always in [0, 1] during a valid episode
t_hours [9+C+1] β elapsed simulation time in hours
Returns float32 to match observation_space.dtype.
"""
X_t = self._current_X()
return np.concatenate([
self._h, # 9 β component healths (may be < 0 stochastic)
X_t, # C β current operating conditions
[self._budget / self.W], # 1 β remaining budget fraction β [0, 1]
[self._t], # 1 β elapsed hours
]).astype(np.float32)
def _current_X(self) -> np.ndarray:
"""
Return the operating-condition vector for the current simulation step.
Clamps the index to the last row of X_series if the episode outlasts
the provided forecast horizon, so the environment never raises an
IndexError regardless of episode length.
"""
idx = min(self._step_idx, len(self.X_series) - 1)
return self.X_series[idx]
# ---------------------------------------------------------------------------
# Training
# ---------------------------------------------------------------------------
def train(
env: PrinterEnv,
*,
total_timesteps: int = 1_000_000,
save_path: str = "scheduler_ppo",
learning_rate: float = 3e-4,
n_steps: int = 2048,
batch_size: int = 64,
n_epochs: int = 10,
gamma: float = 0.99,
ent_coef: float = 0.01,
verbose: int = 1,
) -> PPO:
"""
Train a PPO agent on PrinterEnv and save the result to disk.
Architecture
------------
Both the actor and critic share the same MLP topology
(two hidden layers of 64 units with Tanh activations) but have
separate weights, as is standard in Actor-Critic methods:
Actor (Ο_ΞΈ): obs(20) β 64 β 64 β logits(512) β Softmax
Critic (V_Ο): obs(20) β 64 β 64 β scalar(1)
The 512 Softmax output over the full 2^9 action space implicitly models
the joint probability distribution over all replacement combinations,
capturing correlations (e.g. replacing component 0 should reduce the
probability of also replacing component 1 if they interact positively)
without requiring an autoregressive sampling pass.
Initialisation
--------------
SB3 applies orthogonal initialisation to all layers (scale β2 for hidden,
scale 0.01 for the final policy layer). With scale 0.01 the logits start
near zero, so Softmax(~0) β 1/512 β effectively maximum entropy over the
action space, ensuring the agent explores broadly before committing.
Hyperparameters
---------------
learning_rate : Adam step size (3e-4 is a reliable PPO default).
n_steps : Rollout length before each PPO update (2048 steps β
one to several full episodes depending on episode length).
batch_size : Mini-batch size for gradient updates.
n_epochs : Number of gradient passes over each collected rollout.
gamma : Discount factor; 0.99 weights future rewards heavily,
encouraging the agent to maximise long-term lifespan.
ent_coef : Entropy bonus coefficient; keeps action probabilities from
collapsing to a single action too early in training.
Parameters
----------
env : Configured PrinterEnv instance.
total_timesteps : Total environment steps to train for.
save_path : File path (without .zip) for the saved model.
learning_rate : Adam learning rate.
n_steps : Rollout buffer size (steps per PPO update).
batch_size : SGD mini-batch size.
n_epochs : PPO epochs per rollout.
gamma : Discount factor Ξ³.
ent_coef : Entropy regularisation coefficient.
verbose : SB3 verbosity level (0=silent, 1=info, 2=debug).
Returns
-------
PPO : The trained Stable-Baselines3 PPO model, ready for evaluate().
"""
policy_kwargs = dict(
net_arch=dict(pi=[64, 64], vf=[64, 64]),
activation_fn=th.nn.Tanh,
)
ppo = PPO(
policy="MlpPolicy",
env=env,
learning_rate=learning_rate,
n_steps=n_steps,
batch_size=batch_size,
n_epochs=n_epochs,
gamma=gamma,
ent_coef=ent_coef,
policy_kwargs=policy_kwargs,
verbose=verbose,
)
ppo.learn(total_timesteps=total_timesteps)
ppo.save(save_path)
if verbose:
print(f"[train] Model saved to {save_path}.zip")
return ppo
# ---------------------------------------------------------------------------
# Evaluation
# ---------------------------------------------------------------------------
def evaluate(
ppo: PPO,
env: PrinterEnv,
n_episodes: int = 10,
) -> dict:
"""
Run the trained policy deterministically and return summary statistics.
Each episode starts from a fresh reset() call. The policy is queried with
deterministic=True, meaning the action with the highest probability under
the current Softmax distribution is always selected (no sampling noise).
This gives a reproducible, greedy estimate of the policy's performance.
Parameters
----------
ppo : Trained PPO model returned by train().
env : PrinterEnv instance (can be the same env used for training).
n_episodes : Number of evaluation episodes to average over.
Returns
-------
dict with keys:
mean_hours β average hours survived across all episodes.
std_hours β standard deviation of hours survived.
mean_replacements β average total number of component replacements
performed per episode (summed over all steps).
mean_budget_spent β average euros spent on replacements per episode.
episodes β list of per-episode dicts, each containing:
episode, hours_survived, budget_spent, replacements.
"""
hours, n_replacements, budget_spent = [], [], []
episodes = []
for ep in range(n_episodes):
obs, _ = env.reset()
done = False
ep_replacements = 0
while not done:
action, _ = ppo.predict(obs, deterministic=True)
obs, _, terminated, truncated, _ = env.step(int(action))
done = terminated or truncated
ep_replacements += int(_ACTION_TABLE[int(action)].sum())
hours.append(env._t)
n_replacements.append(ep_replacements)
budget_spent.append(env.W - env._budget)
episodes.append({
"episode": ep,
"hours_survived": env._t,
"budget_spent": env.W - env._budget,
"replacements": ep_replacements,
})
return {
"mean_hours": float(np.mean(hours)),
"std_hours": float(np.std(hours)),
"mean_replacements": float(np.mean(n_replacements)),
"mean_budget_spent": float(np.mean(budget_spent)),
"episodes": episodes,
}
# ---------------------------------------------------------------------------
# Sanity demo
# ---------------------------------------------------------------------------
if __name__ == "__main__":
from process_inputs import process_inputs
deg_model = DegradationModel.load("model.npz")
print(f"Loaded model.npz N={deg_model.N} C={deg_model.C}")
# Representative operating-condition scenarios in natural units (matches phase2.py SCENARIOS).
# Each row: [ambient_temp_c, chamber_temp_c, humidity_pct, contamination_aqi,
# print_hours, build_volume_cm3, recoating_speed_mm_s, recoating_cycles, maintenance_level]
_SCENARIO_CONDITIONS = np.array([
[ 22.0, 180.0, 40.0, 20.0, 56.0, 4500.0, 100.0, 5000.0, 0.10], # nominal
[ 22.0, 180.0, 45.0, 150.0, 56.0, 4500.0, 100.0, 5000.0, 0.20], # high contamination
[ 28.0, 185.0, 50.0, 80.0, 168.0, 13500.0, 120.0, 15000.0, 0.20], # 24/7 heavy use
[ 20.0, 175.0, 30.0, 5.0, 300.0, 3000.0, 90.0, 3500.0, 0.05], # optimal lab
[ 40.0, 200.0, 55.0, 60.0, 56.0, 4500.0, 100.0, 5000.0, 0.20], # hot environment
[ 22.0, 180.0, 85.0, 30.0, 56.0, 4500.0, 100.0, 5000.0, 0.15], # high humidity
[ 25.0, 182.0, 45.0, 40.0, 56.0, 4500.0, 100.0, 5000.0, 0.90], # neglected maintenance
[ 38.0, 195.0, 20.0, 200.0, 80.0, 6500.0, 110.0, 7000.0, 0.40], # desert factory
], dtype=np.float64)
# Build an 8 000-step X_series by cycling through scenarios with small noise
rng = np.random.default_rng(42)
T = 8_000
base_rows = _SCENARIO_CONDITIONS[np.arange(T) % len(_SCENARIO_CONDITIONS)]
noise = rng.normal(0.0, 0.02, size=base_rows.shape) * base_rows # 2% relative noise
X_natural = np.clip(base_rows + noise, 0.0, None)
X_series = np.stack([process_inputs(row) for row in X_natural]) # (T, C) normalised
env = PrinterEnv(
model=deg_model,
X_series=X_series,
W=10_000.0,
dt=1.0,
stochastic=True,
seed=42,
)
print("Observation space:", env.observation_space.shape)
print("Action space: ", env.action_space.n, "discrete actions")
print()
# --- Random-policy baseline ---
obs, _ = env.reset(seed=0)
done = False
while not done:
action = env.action_space.sample()
obs, _, terminated, truncated, info = env.step(action)
done = terminated or truncated
print(f"Random policy β {env._t:.0f} h survived | β¬{env.W - env._budget:.0f} spent")
# --- PPO training (short demo: 200k steps) ---
print("\nTraining PPO (200 000 timesteps) ...")
trained = train(
env,
total_timesteps=200_000,
save_path="scheduler_ppo",
verbose=1,
)
# --- Evaluation ---
results = evaluate(trained, env, n_episodes=10)
print(f"\n{'β'*45}")
print(f" Mean hours survived : {results['mean_hours']:>8.1f} h")
print(f" Std hours : {results['std_hours']:>8.1f} h")
print(f" Mean replacements : {results['mean_replacements']:>8.1f}")
print(f" Mean budget spent : β¬{results['mean_budget_spent']:>7.0f}")
print(f"{'β'*45}")
|