214 lines
9.1 KiB
Python
214 lines
9.1 KiB
Python
"""Pure-Python small grey-box thermal model and binary model predictive control.
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No Home Assistant imports; this module can be tested in isolation. Step=5 minutes.
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This is an experimental thermal model, not a certified boiler controller.
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"""
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from __future__ import annotations
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from dataclasses import dataclass, field
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from itertools import product
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from math import exp, isfinite
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from typing import Any
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STEP_MINUTES = 5
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HEAT_LAG = 1.0 - exp(-STEP_MINUTES / 20.0)
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def bound(value: float, lo: float, hi: float) -> float:
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return max(lo, min(hi, value))
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@dataclass
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class Learner:
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"""Recursive least squares for dT=a*(Tout-T)+b*effective_heat+c."""
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theta: list[float] = field(default_factory=lambda: [0.002, 0.045, 0.0])
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p: list[list[float]] = field(default_factory=lambda: [[0.0005, 0., 0.], [0., 0.8, 0.], [0., 0., 0.08]])
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count: int = 0
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error_sum: float = 0.0
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on_count: int = 0
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off_count: int = 0
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def predict_delta(self, temp: float, outside: float, heat: float) -> float:
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a, b, c = self.theta
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return a * (outside - temp) + b * heat + c
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def learn(self, temp_before: float, temp_after: float, outside: float, effective_heat: float,
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duration_seconds: float = 300, command: bool | None = None) -> bool:
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if not all(isfinite(x) for x in (temp_before, temp_after, outside, effective_heat)):
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return False
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if not 0 <= effective_heat <= 1:
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return False
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if not isfinite(duration_seconds) or not 270 <= duration_seconds <= 330:
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return False
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y = (temp_after - temp_before) * 300 / duration_seconds
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if abs(y) > 0.8: # sensor glitch/door opened/restarted device
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return False
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x = [outside - temp_before, effective_heat, 1.0]
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predicted = sum(t * v for t, v in zip(self.theta, x))
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residual = y - predicted
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px = [sum(self.p[i][j] * x[j] for j in range(3)) for i in range(3)]
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forgetting = 0.999
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denominator = forgetting + sum(x[i] * px[i] for i in range(3))
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if not isfinite(denominator) or denominator <= 0:
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return False
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k = [value / denominator for value in px]
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self.theta = [t + k[i] * residual for i, t in enumerate(self.theta)]
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for i in range(3):
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for j in range(3):
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self.p[i][j] = (self.p[i][j] - k[i] * px[j]) / forgetting
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# Physical constraints; avoids unstable temperature predictions.
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self.theta = [
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bound(self.theta[0], 0.0, 0.04),
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bound(self.theta[1], 0.0, 0.25),
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bound(self.theta[2], -0.06, 0.06),
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]
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self.count += 1
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self.error_sum += abs(residual)
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if command is not None:
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if command:
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self.on_count += 1
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else:
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self.off_count += 1
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return True
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@property
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def mae(self) -> float | None:
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return self.error_sum / self.count if self.count else None
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def as_dict(self) -> dict[str, Any]:
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return {"theta": self.theta, "p": self.p, "count": self.count, "error_sum": self.error_sum,
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"on_count": self.on_count, "off_count": self.off_count}
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@classmethod
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def from_dict(cls, source: dict[str, Any]) -> "Learner":
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obj = cls()
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try:
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if not isinstance(source, dict):
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return obj
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theta = [float(v) for v in source["theta"]]
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p = [[float(v) for v in r] for r in source["p"]]
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if len(theta) != 3 or len(p) != 3 or any(len(r) != 3 for r in p):
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return obj
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if not all(isfinite(v) for v in theta + [v for row in p for v in row]):
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return obj
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if not (0 <= theta[0] <= .04 and 0 <= theta[1] <= .25 and -.06 <= theta[2] <= .06):
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return obj
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# A covariance must be symmetric positive definite (Cholesky check).
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lower = [[0.0] * 3 for _ in range(3)]
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for i in range(3):
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for j in range(i + 1):
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if abs(p[i][j] - p[j][i]) > 1e-8:
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return obj
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value = p[i][j] - sum(lower[i][k] * lower[j][k] for k in range(j))
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if i == j:
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if value <= 0 or not isfinite(value):
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return obj
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lower[i][j] = value ** .5
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else:
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lower[i][j] = value / lower[j][j]
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counts = [source.get(key, 0) for key in ("count", "on_count", "off_count")]
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if any(type(v) is not int or v < 0 for v in counts):
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return obj
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count, on_count, off_count = counts
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error_sum = float(source.get("error_sum", 0))
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if not isfinite(error_sum) or error_sum < 0 or on_count + off_count > count:
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return obj
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return cls(theta, p, count, error_sum, on_count, off_count)
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except (KeyError, TypeError, ValueError, OverflowError):
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return obj
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def simulate_step(temps: dict[str, float], outside: float, lag: float,
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command: bool, learners: dict[str, Learner]) -> tuple[dict[str, float], float]:
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next_lag = lag + HEAT_LAG * (float(command) - lag)
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new = {name: value + learners[name].predict_delta(value, outside, next_lag)
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for name, value in temps.items()}
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return new, next_lag
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def optimize(
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temps: dict[str, float], outside: float, effective_heat: float,
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target: float, weights: dict[str, float], learners: dict[str, Learner],
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is_on: bool, seconds_since_change: float, horizon_minutes: int = 120,
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minimum_on_minutes: int = 15, minimum_off_minutes: int = 10,
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switching_cost: float = .15, heating_cost: float = .025,
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comfort_band: float = .15,
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) -> dict[str, Any]:
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"""Enumerate 15min ON/OFF plans; honor minimum ON/OFF durations.
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120min = 256 plans (fast on Raspberry Pi 5). All rooms share one burner demand.
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"""
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if not temps or set(temps) != set(learners):
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raise ValueError("Missing room temperatures or learner")
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if not 30 <= horizon_minutes <= 180 or horizon_minutes % 15:
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raise ValueError("Horizon must be 30..180 minutes in 15-minute steps")
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if not isfinite(target) or not isfinite(outside):
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raise ValueError("Invalid temperature")
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if any(not isfinite(t) for t in temps.values()):
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raise ValueError("Invalid room temperature")
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if any(not isfinite(float(weights.get(room, 0))) or float(weights.get(room, 0)) <= 0 for room in temps):
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raise ValueError("All rooms need a positive weight")
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if not isfinite(effective_heat) or not 0 <= effective_heat <= 1:
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raise ValueError("Invalid heating lag")
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if any(not isfinite(v) or v < 0 for v in (
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seconds_since_change, minimum_on_minutes, minimum_off_minutes,
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switching_cost, heating_cost, comfort_band,
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)):
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raise ValueError("Invalid optimizer parameter")
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total_weight = sum(float(weights[room]) for room in temps)
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if not isfinite(total_weight):
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raise ValueError("Invalid total weight")
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norm = {room: float(weights[room]) / total_weight for room in temps}
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blocks = horizon_minutes // 15
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nsteps_per_block = 3
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best = float("inf")
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result = None
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min_on_s = minimum_on_minutes * 60
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min_off_s = minimum_off_minutes * 60
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elapsed_initial = max(0.0, seconds_since_change)
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# More sequences than 4096 are deliberately excluded by horizon validation.
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for bits in product((False, True), repeat=blocks):
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current = bool(is_on)
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elapsed_s = elapsed_initial
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state = dict(temps)
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lag = effective_heat
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cost = 0.0
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at_60 = None
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feasible = True
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for idx, bit in enumerate(bits):
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if bit != current:
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minimum = min_on_s if current else min_off_s
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if elapsed_s < minimum:
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feasible = False
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break
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cost += switching_cost
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elapsed_s = 0.0
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current = bit
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for tick in range(nsteps_per_block):
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state, lag = simulate_step(state, outside, lag, bit, learners)
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mismatch = sum(
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norm[room] * max(0.0, abs(value - target) - comfort_band) ** 2
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for room, value in state.items()
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)
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# A lower bound on weighted average comfort also matters.
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avg = sum(norm[r] * value for r, value in state.items())
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mismatch += max(0.0, abs(avg - target) - comfort_band) ** 2
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cost += 8.0 * mismatch + (heating_cost if bit else 0.0)
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if idx * 15 + (tick + 1) * STEP_MINUTES == 60:
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at_60 = dict(state)
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elapsed_s += 15 * 60
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if feasible and cost < best:
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best = cost
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result = (bits, at_60 or {}, dict(state))
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if result is None:
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raise RuntimeError("No feasible schedule")
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plan, temps_60m, temps_end = result
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return {
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"proposal": bool(plan[0]),
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"plan_15min": [int(v) for v in plan],
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"predicted_60m": {r: round(t, 3) for r, t in temps_60m.items()},
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"predicted_end": {r: round(t, 3) for r, t in temps_end.items()},
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"cost": round(best, 4),
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}
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