eomsangdonandClaude Opus 5.5
37011b4a60
- Engine_Prob: 변수 c · φ · γ · 지하수위 이동 · r_u · c–φ 상관(촐레스키) · 고정면 = 절편 기하 한 번 · 물성 칸만 갈아 묶음 평가 (1000 회 0.2 s) · 매회 탐색 = analyze 다시(일꾼 프로세스 풀) · 결과 평균 · σ · Pf · β 정규 · 대수정규(Slide2 식) · 히스토그램 · 누적분포 · P(F < 기준) · 민감도 50 등분 · 토네이도 - 시험 test_537_1_e03_prob 11: 무한사면 해석해(MIT App.17 Pf 0.2257 · LHS 1만 ±2 %) · tanφ 정규 Φ(−β) · 고정면 절편 = 닫힌 꼴 · Slide2 Tutorial 08 · #36(r_u) · 시드 재현 · LHS 층 · 절단 · 대수정규 · 민감도 · 매회 탐색 Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
442 lines
17 KiB
Python
442 lines
17 KiB
Python
"""E03 2D 확률 해석 · 민감도 (요구 351 · PLAN 537-1) — Slide2 · SLOPE/W Probabilistic 과 같은 생각.
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확률 변수 = 물성(c · φ · γ) · 지하수위(수위선 위아래 이동 m) · r_u — 정규 · 대수정규 · 절단(평균 아래 · 위
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거리 = Slide2 Relative Min · Max · 물리 한계 c ≥ 0 · 0 ≤ φ < 89 · γ > 0 · 0 ≤ r_u < 1 도 절단) · 변수 사이 상관
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(Slide2 c–φ Correlation · 표준정규에서 촐레스키) → 몬테카를로 · 라틴 하이퍼큐브 N 회
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→ 안전율 표본 → 평균 · 표준편차 · Pf = P(F < 1) · β 정규 (μ − 1)/σ · β 대수정규
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ln(μ/√(1+V²))/√ln(1+V²) · 히스토그램 · 누적분포 · P(F < 기준안전율).
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갈래: fixed = 결정론 임계면 고정(절편 기하 한 번 · 물성만 바꿔 묶음 평가 · 빠름 · Slide2 Global Minimum) ·
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search = 표본마다 임계면 다시 찾음(`Engine_Search.analyze` · 느림 · 프로세스 병렬 · Slide2 Overall Slope).
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민감도 = 변수 하나씩 범위(절단 끝 · 없으면 ±3σ) 50 등분 훑기(나머지 평균 · 임계면 고정 · Slide2 Sensitivity 와 같음)
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· 토네이도 = 끝값 F 폭 순.
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γ 변수 = γt 표본 · γsat 는 같은 차만큼 옮김(γsat − γt 그대로).
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search 일꾼 = `python -m E03_StabSection.E03_StabSection_Engine_Prob <job.json>`(서버 프로세스에서 풀을 열지 않음 ·
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`Worker` 머리글) · 한 줄마다 {"done": n} · 끝에 job["out"] 파일.
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NumPy · SciPy(stats) 만 · 계산 자리 = ③ 서버 단독.
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"""
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from __future__ import annotations
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import copy
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import json
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import math
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import sys
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import time
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from pathlib import Path
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import numpy as np
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from scipy.stats import norm
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from E03_StabSection import E03_StabSection_Engine_LEM as lem
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from E03_StabSection.E03_StabSection_Engine_Search import analyze
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from E03_StabSection.E03_StabSection_Engine_Station import MIN_DEPTH_M
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from E03_StabSection.E03_StabSection_Engine_Surface import (
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circle_slices,
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evaluate,
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poly_slices,
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three_point_center,
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)
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PROPS = ("c", "phi", "gamma", "water", "ru")
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#: 물리 한계(절단) — 지하수 이동은 한계 없음
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BOUNDS = {"c": (0.0, math.inf), "phi": (0.0, 89.0), "gamma": (1e-3, math.inf), "ru": (0.0, 0.99)}
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#: 절단 없을 때 민감도 훑기 범위(±σ 배)
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SWEEP_SIGMA = 3.0
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SWEEP_POINTS = 51
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HIST_BINS = 30
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CDF_POINTS = 101
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N_SLICES = 50
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# ---- 분포 · 표본 --------------------------------------------------------------
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def _bounds(v: dict) -> tuple[float, float]:
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"""절단 구간 [a, b] — 평균 ∓ 아래 · 위 거리 ∩ 물리 한계."""
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lo_phys, hi_phys = BOUNDS.get(v["prop"], (-math.inf, math.inf))
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mean = float(v["mean"])
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a = mean - float(v["lo"]) if v.get("lo") is not None else -math.inf
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b = mean + float(v["hi"]) if v.get("hi") is not None else math.inf
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return max(a, lo_phys), min(b, hi_phys)
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def _lognormal(v: dict) -> tuple[float, float]:
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"""대수정규 (μ_ln, σ_ln) — 평균 · 표준편차 그대로 맞춤."""
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mean, std = float(v["mean"]), float(v["std"])
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s2 = math.log1p((std / mean) ** 2)
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return math.log(mean) - 0.5 * s2, math.sqrt(s2)
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def ppf(v: dict, u: np.ndarray) -> np.ndarray:
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"""균등 u(0~1) → 변수 값(절단 분포 역함수)."""
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u = np.asarray(u, float)
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mean, std = float(v["mean"]), float(v.get("std") or 0.0)
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if std <= 0:
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return np.full(u.shape, mean)
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a, b = _bounds(v)
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if v.get("dist") == "lognormal" and v["prop"] != "water":
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if mean <= 0:
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raise ValueError(f"대수정규는 평균 > 0: {v}")
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mu, s = _lognormal(v)
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za = (math.log(a) - mu) / s if a > 0 else -math.inf
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zb = (math.log(b) - mu) / s if b < math.inf else math.inf
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pa, pb = norm.cdf(za), norm.cdf(zb)
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return np.exp(mu + s * norm.ppf(pa + u * (pb - pa)))
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pa, pb = norm.cdf((a - mean) / std), norm.cdf((b - mean) / std)
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return mean + std * norm.ppf(pa + u * (pb - pa))
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def sample(
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variables: list[dict],
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n: int,
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*,
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sampling: str = "lhs",
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seed: int = 0,
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correlations: list | None = None,
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) -> np.ndarray:
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"""표본 (n, 변수 수) — lhs = 라틴 하이퍼큐브(변수마다 n 칸 하나씩 · 칸 차례 섞음) · mc = 단순 무작위.
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correlations = [(i, j, ρ), …] — 표준정규 칸에서 촐레스키로 섞은 뒤 분포로(LHS 층은 섞인 변수만 흐려짐)."""
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rng = np.random.default_rng(int(seed))
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k = len(variables)
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if sampling == "lhs":
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order = np.argsort(rng.random((n, k)), axis=0)
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u = (order + rng.random((n, k))) / n
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else:
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u = rng.random((n, k))
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u = np.clip(u, 1e-12, 1 - 1e-12)
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if correlations:
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corr = np.eye(k)
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for i, j, rho in correlations:
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corr[i, j] = corr[j, i] = float(rho)
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u = norm.cdf(norm.ppf(u) @ np.linalg.cholesky(corr).T)
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u = np.clip(u, 1e-12, 1 - 1e-12)
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return np.column_stack([ppf(v, u[:, j]) for j, v in enumerate(variables)]) if k else u
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def sweep_range(v: dict) -> tuple[float, float]:
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"""민감도 훑기 범위 — 절단 끝 · 없으면 평균 ±3σ(물리 한계 안)."""
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mean, std = float(v["mean"]), float(v.get("std") or 0.0)
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a, b = _bounds(v)
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lo = a if math.isfinite(a) and v.get("lo") is not None else mean - SWEEP_SIGMA * std
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hi = b if math.isfinite(b) and v.get("hi") is not None else mean + SWEEP_SIGMA * std
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lo_phys, hi_phys = BOUNDS.get(v["prop"], (-math.inf, math.inf))
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return max(lo, lo_phys), min(hi, hi_phys)
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# ---- 통계 -------------------------------------------------------------------
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def statistics(F: np.ndarray, required: float | None = None, bins: int = HIST_BINS) -> dict:
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"""안전율 표본 → 평균 · 표준편차 · Pf · β 정규 · 대수정규 · 히스토그램 · 누적분포(해 없는 표본 = 셈 밖)."""
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F = np.asarray(F, float)
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ok = F[np.isfinite(F)]
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out = {"n": int(len(F)), "n_valid": int(len(ok))}
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if len(ok) < 2:
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return {**out, "mean": None, "std": None, "pf": None, "beta_normal": None}
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mean, std = float(ok.mean()), float(ok.std(ddof=1))
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V = std / mean if mean > 0 else math.nan
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beta_ln = (
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math.log(mean / math.sqrt(1 + V * V)) / math.sqrt(math.log1p(V * V))
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if mean > 0 and V > 0
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else None
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)
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counts, edges = np.histogram(ok, bins=bins)
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p = np.linspace(0.0, 1.0, CDF_POINTS)
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out.update(
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mean=mean,
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std=std,
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cov=V if math.isfinite(V) else None,
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min=float(ok.min()),
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max=float(ok.max()),
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pf=float(np.mean(ok < 1.0)),
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n_fail=int(np.sum(ok < 1.0)),
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beta_normal=(mean - 1.0) / std if std > 0 else None,
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beta_lognormal=beta_ln,
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required=required,
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p_below_required=float(np.mean(ok < required)) if required else None,
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histogram={"edges": edges.tolist(), "counts": counts.tolist()},
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cdf={"p": p.tolist(), "F": np.quantile(ok, p).tolist()},
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)
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return out
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# ---- 변수 → 모형 ---------------------------------------------------------------
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def perturb(model: dict, variables: list[dict], row) -> dict:
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"""모형 사본 — 표본 한 줄을 물성 · 지하수위에 넣음(search 갈래)."""
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out = dict(model)
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mats = {m["id"]: dict(m) for m in model["materials"]}
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dz = 0.0
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for v, x in zip(variables, row):
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if v["prop"] == "water":
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dz += float(x)
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continue
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if v["prop"] == "ru":
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gw = model.get("groundwater") or {}
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if gw.get("mode") == "ru":
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out["groundwater"] = {**gw, "ru": float(x)}
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continue
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m = mats[v["material"]]
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if v["prop"] == "gamma":
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gt = float(m["gamma_t"])
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m["gamma_sat"] = float(m.get("gamma_sat", gt)) + float(x) - gt
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m["gamma_t"] = float(x)
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else:
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m[v["prop"]] = float(x)
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out["materials"] = list(mats.values())
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gw = out.get("groundwater") or {}
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if dz and gw.get("mode") == "line":
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out["groundwater"] = {**gw, "line": [[x, z + dz] for x, z in gw["line"]]}
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return out
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class Fixed:
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"""임계면 고정 — 모형 · 면 하나를 한 번 준비해 표본마다 물성 칸만 갈아 끼우고 절편 묶음으로 평가."""
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def __init__(self, model: dict, surface: dict, direction: int, n_slices: int = N_SLICES):
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self.prep = lem.Prepared(model, direction)
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self.n = n_slices
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s = self.prep.direction
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self.index = {m["id"]: i for i, m in enumerate(self.prep.materials)}
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if surface["kind"] == "circle":
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xs = sorted((s * surface["entry"][0], s * surface["exit"][0]))
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self.geom = (
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"circle",
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s * surface["center"][0],
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surface["center"][1],
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surface["radius"],
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)
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self.geom += tuple(xs)
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else:
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pts = sorted((s * x, z) for x, z in surface["points"])
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self.geom = ("polyline", np.array([p[0] for p in pts]), np.array([p[1] for p in pts]))
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def _prep(self, variables: list[dict], row) -> lem.Prepared:
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base = self.prep
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p = copy.copy(base)
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gt, gs = base.gamma_t.copy(), base.gamma_sat.copy()
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c, tp = base.c.copy(), base.tanphi.copy()
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dz = 0.0
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for v, x in zip(variables, row):
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if v["prop"] == "water":
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dz += float(x)
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continue
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if v["prop"] == "ru":
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if base.gw_mode == "ru":
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p.ru = float(x)
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continue
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i = self.index[v["material"]]
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if v["prop"] == "c":
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c[i] = x
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elif v["prop"] == "phi":
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tp[i] = math.tan(math.radians(x))
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else:
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gs[i] += x - gt[i]
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gt[i] = x
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p.gamma_t, p.gamma_sat, p.c, p.tanphi = gt, gs, c, tp
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p.table = base.table.copy()
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p.table[:, 4, :] = gt[base.mat]
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p.table[:, 5, :] = gs[base.mat] - gt[base.mat]
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if dz and base.gw_mode == "line":
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p.water_z = base.water_z + dz
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return p
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def _slices(self, prep: lem.Prepared) -> tuple[dict, np.ndarray]:
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g = self.geom
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if g[0] == "circle":
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_, xc, zc, R, xE, xX = g
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sl = circle_slices(prep, [xc], [zc], [R], [xE], [xX], self.n)
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return sl, np.array([[xc, zc]])
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vx, vz = g[1][None, :], g[2][None, :]
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return poly_slices(prep, vx, vz, self.n), three_point_center(vx, vz)
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def F(self, variables: list[dict], X: np.ndarray, method: str) -> np.ndarray:
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"""표본 줄마다 안전율(해 없음 = nan)."""
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X = np.atleast_2d(np.asarray(X, float))
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parts = [self._slices(self._prep(variables, row)) for row in X]
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sl = _stack([p[0] for p in parts])
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center = np.vstack([p[1] for p in parts])
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mp_seed = None
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if method == "morgenstern_price": # describe 와 같은 출발 참고값(같은 면 Spencer)
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mp_seed = evaluate(sl, center, ("spencer",))["spencer"]["F"]
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sl.pop("_pre", None)
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F = evaluate(sl, center, (method,), mp_seed=mp_seed)[method]["F"]
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return np.where(sl["valid"], F, np.nan)
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def _stack(parts: list[dict]) -> dict:
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"""한 줄짜리 절편 묶음들 → (S, …) 하나(배열 칸만 잇고 스칼라는 그대로)."""
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out = {}
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for key, value in parts[0].items():
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if key == "_pre":
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continue
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if isinstance(value, np.ndarray) and value.ndim >= 1 and value.shape[0] == 1:
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out[key] = np.concatenate([p[key] for p in parts])
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else:
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out[key] = value
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return out
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def _chunks(n: int, size: int):
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for i in range(0, n, size):
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yield slice(i, min(i + size, n))
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def sensitivity(
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fixed: Fixed, variables: list[dict], method: str, points: int = SWEEP_POINTS
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) -> dict:
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"""변수 하나씩 범위 훑기(나머지 평균) · 토네이도 = 끝값 F 폭 큰 순."""
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means = np.array([float(v["mean"]) for v in variables])
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rows, spans = [], []
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for j, v in enumerate(variables):
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lo, hi = sweep_range(v)
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xs = np.linspace(lo, hi, points) if hi > lo else np.full(points, means[j])
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block = np.tile(means, (points, 1))
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block[:, j] = xs
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rows.append(block)
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spans.append(xs)
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F0 = float(fixed.F(variables, means[None, :], method)[0])
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if not rows:
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return {"F_mean": F0, "curves": [], "tornado": []}
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F = fixed.F(variables, np.vstack(rows), method).reshape(len(variables), points)
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num = lambda a: [float(x) if np.isfinite(x) else None for x in a] # noqa: E731
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curves = []
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for v, xs, f in zip(variables, spans, F):
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ends = [f[0], f[-1]]
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swing = abs(ends[1] - ends[0]) if all(np.isfinite(ends)) else None
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curves.append(
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{
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"name": v["name"],
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"x": num(xs),
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"F": num(f),
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"F_lo": num([ends[0]])[0],
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"F_hi": num([ends[1]])[0],
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"swing": swing,
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}
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)
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tornado = sorted(
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(c for c in curves if c["swing"] is not None), key=lambda c: c["swing"], reverse=True
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)
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return {"F_mean": F0 if math.isfinite(F0) else None, "curves": curves, "tornado": [
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{"name": c["name"], "F_lo": c["F_lo"], "F_hi": c["F_hi"], "swing": c["swing"]}
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for c in tornado
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]} # fmt: skip
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# ---- 매회 탐색(search) ------------------------------------------------------------
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_CTX: dict = {}
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def _init(ctx: dict) -> None:
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_CTX.clear()
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_CTX.update(ctx)
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def _search_one(row) -> float:
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c = _CTX
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m = c["method"]
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||
methods = tuple(dict.fromkeys(("bishop", m)))
|
||
res = analyze(
|
||
perturb(c["model"], c["variables"], row),
|
||
direction=c["direction"],
|
||
limits=c["limits"],
|
||
methods=methods,
|
||
noncircular=m not in ("ordinary", "bishop"), # 비원호 Fellenius · Bishop = 참고 칸
|
||
min_depth=MIN_DEPTH_M,
|
||
)
|
||
best = res["methods"][m]["min"]
|
||
return float(best["F"]) if best and best.get("F") is not None else math.nan
|
||
|
||
|
||
def search_F(ctx: dict, X: np.ndarray, workers: int = 1, emit=None) -> np.ndarray:
|
||
"""표본마다 임계면 다시 찾음 — workers > 1 = 프로세스 풀(서버 밖 일꾼에서만)."""
|
||
out = np.full(len(X), np.nan)
|
||
if workers <= 1:
|
||
_init(ctx)
|
||
for i, row in enumerate(X):
|
||
out[i] = _search_one(row)
|
||
emit and emit(i + 1)
|
||
return out
|
||
from concurrent.futures import ProcessPoolExecutor, as_completed
|
||
|
||
with ProcessPoolExecutor(max_workers=workers, initializer=_init, initargs=(ctx,)) as pool:
|
||
futures = {pool.submit(_search_one, row): i for i, row in enumerate(X)}
|
||
for done, future in enumerate(as_completed(futures), 1):
|
||
out[futures[future]] = future.result()
|
||
emit and emit(done)
|
||
return out
|
||
|
||
|
||
# ---- 한 번 해석 ---------------------------------------------------------------
|
||
def run(
|
||
model: dict,
|
||
*,
|
||
surface: dict,
|
||
direction: int,
|
||
limits=None,
|
||
variables: list[dict],
|
||
correlations: list | None = None,
|
||
n: int = 1000,
|
||
sampling: str = "lhs",
|
||
seed: int = 0,
|
||
mode: str = "fixed",
|
||
method: str = "bishop",
|
||
required: float | None = None,
|
||
workers: int = 1,
|
||
emit=None,
|
||
) -> dict:
|
||
"""확률 해석 + 민감도 한 벌. emit(끝난 표본 수) = 진행률."""
|
||
t0 = time.perf_counter()
|
||
X = sample(variables, n, sampling=sampling, seed=seed, correlations=correlations)
|
||
fixed = Fixed(model, surface, direction)
|
||
t1 = time.perf_counter()
|
||
if mode == "search":
|
||
ctx = {
|
||
"model": model,
|
||
"variables": variables,
|
||
"direction": direction,
|
||
"limits": limits,
|
||
"method": method,
|
||
}
|
||
F = search_F(ctx, X, workers, emit)
|
||
else:
|
||
F = np.full(n, np.nan)
|
||
for part in _chunks(n, 250):
|
||
F[part] = fixed.F(variables, X[part], method)
|
||
emit and emit(part.stop)
|
||
t2 = time.perf_counter()
|
||
sens = sensitivity(fixed, variables, method)
|
||
t3 = time.perf_counter()
|
||
realized = [
|
||
{"name": v["name"], "mean": float(X[:, j].mean()), "std": float(X[:, j].std(ddof=1))}
|
||
for j, v in enumerate(variables)
|
||
]
|
||
return {
|
||
"mode": mode,
|
||
"method": method,
|
||
"n": n,
|
||
"sampling": sampling,
|
||
"seed": seed,
|
||
"variables": variables,
|
||
"correlations": correlations or [],
|
||
"realized": realized,
|
||
"stats": statistics(F, required),
|
||
"F": [round(float(f), 4) if np.isfinite(f) else None for f in F],
|
||
"sensitivity": sens,
|
||
"elapsed_s": {
|
||
"prepare": round(t1 - t0, 3),
|
||
"samples": round(t2 - t1, 3),
|
||
"sensitivity": round(t3 - t2, 3),
|
||
"total": round(t3 - t0, 3),
|
||
},
|
||
}
|
||
|
||
|
||
def main() -> None:
|
||
"""일꾼 — job = run() 인자 + out(결과 파일) · 한 줄마다 진행."""
|
||
path = Path(sys.argv[1])
|
||
job = json.loads(path.read_text(encoding="utf-8"))
|
||
out = Path(job.pop("out"))
|
||
result = run(**job, emit=lambda k: print(json.dumps({"done": k}), flush=True))
|
||
out.write_text(json.dumps(result, ensure_ascii=False), encoding="utf-8")
|
||
|
||
|
||
if __name__ == "__main__":
|
||
main()
|