wangyu
193da0018f
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483 lines
22 KiB
Python
483 lines
22 KiB
Python
"""
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工艺预测模型 — 灰箱（Gray-box）架构
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设计思路：
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物理结构来自 Arrhenius 酸洗动力学，参数取自公开文献实验值，
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而非理论推导。每个模型内置校准系数 K_cal（初始=1.0），
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投产后可通过 calibrate() 方法用实测结果回归更新，
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使模型随数据积累逐步收敛到真实工况。
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关键文献依据：
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[1] 碳钢 HCl 酸洗活化能：Ea ≈ 40~50 kJ/mol（实验测定均值取 45 kJ/mol）
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来源：Hydrochloric Acid Pickling Process Optimization in Metal Wire,
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IJSSST Vol-16 No-5; IspatGuru Pickling of Hot Rolled Strip
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[2] H⁺ 浓度动力学阶次：1.0~2.0阶（取保守值 1.2）
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来源：Optimizing pickling process for 30Cr13 steel,
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ScienceDirect 2025; neural network MPC studies
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[3] 温度效应校验：速率每升温 6~8°C 翻倍（Ea≈45 kJ/mol 时对应约 7°C）
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[4] 欠酸洗风险判别特征：strip thickness, speed, conc, temp
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来源：Prediction of under pickling defects on steel strip surface,
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arXiv:1207.0911
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[5] 速度优化：Nelder-Mead simplex 已在实际 1450mm 酸洗线验证
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来源：Zhu et al., Advances in Mechanical Engineering, 2016
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"""
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import math
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import json
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import os
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from typing import List, Dict, Any, Optional, Tuple
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# ── 校准系数持久化路径 ────────────────────────────────────────────────────────
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_CAL_FILE = os.path.join(os.path.dirname(__file__), "cal_coeffs.json")
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def _load_cal() -> Dict[str, float]:
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try:
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with open(_CAL_FILE) as f:
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return json.load(f)
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except Exception:
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return {}
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def _save_cal(d: Dict[str, float]):
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with open(_CAL_FILE, "w") as f:
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json.dump(d, f, indent=2)
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# ─────────────────────────────────────────────────────────────────────────────
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# 1. 酸洗速度模型（Gray-box）
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# ─────────────────────────────────────────────────────────────────────────────
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class AcidSpeedModel:
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"""
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基于文献实测参数的 Arrhenius 灰箱模型。
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与上一版本的关键差异：
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- Ea/R: 3000 K → 5413 K（45 kJ/mol 实验值，文献[1]）
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- 浓度指数: 0.6 → 1.2（H⁺ 二阶动力学，文献[2]）
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- 增加氧化铁皮结构修正（FeO/Fe₃O₄双层模型，文献[4]）
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- 内置 K_cal 校准系数，支持投产后在线标定
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"""
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# 文献实验值（碳钢 HCl 连续酸洗）
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TANK_LENGTH = 18.0 # m，单槽有效长度（按设备规格书）
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NUM_TANKS = 6
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# K0 由实际工况反推：
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# 目标：75°C、180 g/L 正常酸液条件下，最大速度约 120~130 m/min（PI≥95%）
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# 推导：t_total = 6×18/(125/60)=51.8s，k=ln(20)/51.8=0.058 s⁻¹
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# k=K0×SCALE_RATE_FACTOR → K0=0.058/0.765≈0.075 s⁻¹
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K0 = 0.075 # 指前因子 s⁻¹，由设备规格反推标定
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EA_R = 5413.0 # Ea/R (K)，Ea=45 kJ/mol / R=8.314（文献实验值[1]）
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T_REF = 348.15 # 参考温度 75°C (K)
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C_REF = 180.0 # 参考游离酸浓度 g/L
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N_CONC = 1.2 # 浓度动力学阶次（文献[2] 取保守值）
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V_MIN = 20.0
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V_MAX = 180.0
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CAL_KEY = "acid_speed_kcal"
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# 氧化铁皮结构系数（FeO 快速溶解 + Fe₃O₄ 慢速溶解，文献[4]）
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# 热轧碳钢铁皮组成约：FeO 70%，Fe₃O₄ 20%，Fe₂O₃ 10%
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# FeO 溶速约为 Fe₃O₄ 的 4 倍；有效速率取加权平均
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SCALE_RATE_FACTOR = 0.70 * 1.0 + 0.20 * 0.25 + 0.10 * 0.15 # ≈ 0.765
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def __init__(
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self,
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thickness: float, # mm
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width: float, # mm
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steel_grade: str,
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acid_conc_list: List[float], # 各槽游离酸 g/L
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acid_temp_list: List[float], # 各槽温度 °C
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scale_weight: float = 8.5, # g/m²，氧化铁皮重量
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target_pi: float = 95.0,
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):
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if len(acid_conc_list) != self.NUM_TANKS:
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raise ValueError(f"acid_conc_list 需要 {self.NUM_TANKS} 个元素")
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if len(acid_temp_list) != self.NUM_TANKS:
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raise ValueError(f"acid_temp_list 需要 {self.NUM_TANKS} 个元素")
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self.thickness = thickness
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self.width = width
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self.steel_grade = steel_grade
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self.acid_conc_list = acid_conc_list
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self.acid_temp_list = acid_temp_list
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self.scale_weight = scale_weight
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self.target_pi = target_pi
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self.K_cal = _load_cal().get(self.CAL_KEY, 1.0)
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def _k_i(self, conc: float, temp_c: float) -> float:
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"""单槽有效酸洗速率常数（含文献参数 + 铁皮结构修正）"""
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T_k = temp_c + 273.15
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arrhenius = math.exp(-self.EA_R * (1.0 / T_k - 1.0 / self.T_REF))
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conc_factor = max(conc / self.C_REF, 0.01) ** self.N_CONC
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# 铁皮越厚，有效接触面积越低（正比于 1/scale_weight^0.3 经验修正）
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scale_corr = (8.5 / max(self.scale_weight, 1.0)) ** 0.3
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return self.K0 * arrhenius * conc_factor * self.SCALE_RATE_FACTOR * scale_corr * self.K_cal
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def _compute_pi(self, v_mpm: float) -> Tuple[float, List[float], List[float]]:
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v_mps = v_mpm / 60.0
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pi_prev = 0.0
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pi_per_tank, rt_per_tank = [], []
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for i in range(self.NUM_TANKS):
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t_i = self.TANK_LENGTH / v_mps
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k_i = self._k_i(self.acid_conc_list[i], self.acid_temp_list[i])
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# 精确解析解：dPI/dt = k*(1-PI/100) → PI_new = 100-(100-PI_old)*exp(-k*t)
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# 避免 Euler 一阶近似在 k*t 较大时的严重失真
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pi_prev = 100.0 - (100.0 - pi_prev) * math.exp(-k_i * t_i)
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pi_per_tank.append(round(pi_prev, 2))
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rt_per_tank.append(round(t_i, 1))
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return pi_prev, pi_per_tank, rt_per_tank
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def calculate(self) -> Dict[str, Any]:
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# Nelder-Mead 单维退化为二分搜索（文献[5]验证有效）
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pi_at_min, _, _ = self._compute_pi(self.V_MIN)
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if pi_at_min < self.target_pi:
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pi, pp, rt = self._compute_pi(self.V_MIN)
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return {
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"max_speed": self.V_MIN,
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"pi_per_tank": pp,
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"residence_time_per_tank": rt,
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"total_pi": round(pi, 2),
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"under_pickling_risk": self._risk_level(self.V_MIN, pi),
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"warning": "酸液条件不足，即使最低速下酸洗指数仍低于目标，请检查酸浓度和温度",
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"K_cal": self.K_cal,
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}
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lo, hi, best_v = self.V_MIN, self.V_MAX, self.V_MIN
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while hi - lo >= 0.5:
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mid = (lo + hi) / 2.0
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pi_mid, _, _ = self._compute_pi(mid)
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if pi_mid >= self.target_pi:
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best_v = mid; lo = mid + 0.5
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else:
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hi = mid - 0.5
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best_v = math.floor(best_v)
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total_pi, pi_per_tank, rt_per_tank = self._compute_pi(best_v)
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return {
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"max_speed": best_v,
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"pi_per_tank": pi_per_tank,
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"residence_time_per_tank": rt_per_tank,
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"total_pi": round(total_pi, 2),
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"under_pickling_risk": self._risk_level(best_v, total_pi),
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"warning": None,
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"K_cal": self.K_cal,
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}
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def _risk_level(self, speed: float, pi: float) -> str:
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"""
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欠酸洗风险评估（文献[4] decision-tree 特征阈值）
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输入：speed(m/min), pi(%)，结合厚度、浓度综合判断
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"""
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avg_conc = sum(self.acid_conc_list) / len(self.acid_conc_list)
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avg_temp = sum(self.acid_temp_list) / len(self.acid_temp_list)
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# 文献给出的欠酸洗高风险条件组合
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risk_score = 0
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if pi < 85: risk_score += 3
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elif pi < 92: risk_score += 1
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if speed > 140: risk_score += 2
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if avg_conc < 120: risk_score += 2
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if avg_temp < 68: risk_score += 2
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if self.thickness > 4.0: risk_score += 1
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if risk_score >= 5: return "HIGH"
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elif risk_score >= 2: return "MEDIUM"
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else: return "LOW"
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def calibrate(self, actual_max_speed: float,
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actual_quality_ok: bool) -> float:
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"""
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投产后标定接口：
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传入某卷的实际最大可用速度（操作员确认质量合格时的速度），
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用简单比例更新 K_cal，使模型逐步向真实工况收敛。
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actual_max_speed: 实际测得质量合格的最高速度 (m/min)
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actual_quality_ok: True=该速度下质量合格，False=出现欠酸洗
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"""
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predicted = self.calculate()["max_speed"]
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if not actual_quality_ok:
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# 预测速度偏高，缩减 K_cal
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adjustment = 0.95
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else:
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ratio = actual_max_speed / max(predicted, 1.0)
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# 平滑更新，避免单次样本过拟合
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adjustment = 1.0 + 0.3 * (ratio - 1.0)
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adjustment = max(0.7, min(1.3, adjustment))
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self.K_cal = round(self.K_cal * adjustment, 4)
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cal = _load_cal()
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cal[self.CAL_KEY] = self.K_cal
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_save_cal(cal)
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return self.K_cal
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# ─────────────────────────────────────────────────────────────────────────────
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# 2. 张力设定模型
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# ─────────────────────────────────────────────────────────────────────────────
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class TensionModel:
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"""
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张力模型：基于截面积×屈服强度，区间比例系数参考酸洗线工程手册。
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每个区段独立校准系数 zone_kcal[zone]，互不干扰。
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"""
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# 各区基准比例系数（酸洗线工程实践均值）
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ZONE_RATIOS = {
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"inlet": 1.00,
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"s1_roller": 0.85,
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"acid_entry": 0.78,
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"acid1": 0.72,
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"acid2": 0.68,
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"acid3": 0.68,
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"rinse": 0.70,
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"leveler": 0.76,
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"s2_roller": 0.88,
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"outlet": 1.00,
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}
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ZONE_NAMES_CN = {
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"inlet": "入口张力辊",
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"s1_roller": "S1夹送辊",
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"acid_entry": "酸洗入口辊",
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"acid1": "1#酸槽",
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"acid2": "2#酸槽",
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"acid3": "3#酸槽",
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"rinse": "漂洗段辊",
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"leveler": "拉矫机",
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"s2_roller": "S2夹送辊",
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"outlet": "出口张力辊",
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}
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@staticmethod
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def _zone_cal_key(zone: str) -> str:
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return f"tension_zone_{zone}"
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def __init__(
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self,
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thickness: float,
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width: float,
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yield_strength: float,
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tension_coef: float = 0.25,
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):
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self.thickness = thickness
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self.width = width
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self.yield_strength = yield_strength
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self.tension_coef = tension_coef
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cal = _load_cal()
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# 每个区段独立加载自己的校准系数，默认 1.0
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self.zone_kcal: Dict[str, float] = {
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z: cal.get(self._zone_cal_key(z), 1.0)
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for z in self.ZONE_RATIOS
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}
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def calculate(self) -> Dict[str, Any]:
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cross_section = self.thickness * self.width # mm²
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# T_max 是理论基准值（不含区段校准，区段校准在各 zone 内单独乘）
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t_base_kn = (self.tension_coef * self.yield_strength
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* cross_section / 1000.0) # kN
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zones = {}
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for zone, ratio in self.ZONE_RATIOS.items():
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k = self.zone_kcal.get(zone, 1.0)
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zones[zone] = {
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"tension_kN": round(t_base_kn * ratio * k, 2),
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"ratio": ratio,
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"k_cal": k,
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"name_cn": self.ZONE_NAMES_CN[zone],
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}
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density = 7850.0
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mass_per_m = density * (self.thickness / 1000.0) * (self.width / 1000.0)
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accel_kn = round(mass_per_m * (30.0 / 60.0) / 1000.0, 3)
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t_max_kn = round(t_base_kn * self.zone_kcal.get("inlet", 1.0), 2)
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return {
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"T_max": t_max_kn,
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"T_base": round(t_base_kn, 2),
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"cross_section_mm2": round(cross_section, 1),
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"zones": zones,
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"weld_speed_limit": 60.0,
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"weld_tension_kN": round(t_max_kn * 0.60, 2),
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"accel_tension": accel_kn,
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"zone_kcal": self.zone_kcal,
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}
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def calibrate(self, zone: str, measured_kn: float) -> Dict[str, float]:
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"""仅更新指定区段的校准系数，其他区段不变"""
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if zone not in self.ZONE_RATIOS:
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raise ValueError(f"未知区段: {zone}")
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t_base = (self.tension_coef * self.yield_strength
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* self.thickness * self.width / 1000.0)
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predicted = t_base * self.ZONE_RATIOS[zone] * self.zone_kcal[zone]
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ratio = measured_kn / max(predicted, 0.1)
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# 平滑更新，步长 40%，范围限制在 [0.5, 2.0]
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adjustment = 1.0 + 0.4 * (ratio - 1.0)
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adjustment = max(0.5, min(2.0, adjustment))
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new_k = round(self.zone_kcal[zone] * adjustment, 4)
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self.zone_kcal[zone] = new_k
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cal = _load_cal()
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cal[self._zone_cal_key(zone)] = new_k
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_save_cal(cal)
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return self.zone_kcal
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# ─────────────────────────────────────────────────────────────────────────────
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# 3. 质量预测模型
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# ─────────────────────────────────────────────────────────────────────────────
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class QualityPredictionModel:
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"""
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欠酸洗风险 + 质量等级预测。
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v2 变化：
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- 使用与 AcidSpeedModel 一致的文献参数（Ea/R=5413, n=1.2）
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- 欠酸洗风险特征阈值参考 arXiv:1207.0911 的 decision-tree 结论
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- 增加铁离子浓度（FeCl₂）对酸洗能力的抑制修正
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- 支持投产后用实际质量等级校准评分阈值
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"""
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EA_R = 5413.0
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T_REF = 348.15
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C_REF = 180.0
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N_CONC = 1.2
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CAL_KEY = "quality_kcal"
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def __init__(
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self,
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thickness: float,
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avg_speed: float,
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acid_conc_avg: float, # 游离酸均值 g/L
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acid_temp_avg: float, # 温度均值 °C
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scale_weight: float = 8.5,
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fe_conc_avg: float = 60.0, # FeCl₂ 浓度 g/L（铁离子抑制效应）
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):
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self.thickness = thickness
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self.avg_speed = avg_speed
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self.acid_conc_avg = acid_conc_avg
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self.acid_temp_avg = acid_temp_avg
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self.scale_weight = scale_weight
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self.fe_conc_avg = fe_conc_avg
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self.K_cal = _load_cal().get(self.CAL_KEY, 1.0)
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def _pickling_index_score(self) -> float:
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T_k = self.acid_temp_avg + 273.15
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arrhenius = math.exp(-self.EA_R * (1.0 / T_k - 1.0 / self.T_REF))
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conc_factor = max(self.acid_conc_avg / self.C_REF, 0.01) ** self.N_CONC
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# 铁离子抑制：FeCl₂ > 80 g/L 时显著降低酸洗速率（文献经验）
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fe_inhibition = 1.0 - max(0.0, (self.fe_conc_avg - 80.0) / 200.0) * 0.35
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scale_corr = (8.5 / max(self.scale_weight, 1.0)) ** 0.3
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exposure = (1.20 * arrhenius * conc_factor * fe_inhibition
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||
* scale_corr * 18.0 * 6) / (self.avg_speed / 60.0)
|
||
pi_score = 100.0 * (1.0 - math.exp(-exposure / 10.0))
|
||
return min(max(pi_score * self.K_cal, 0.0), 100.0)
|
||
|
||
def _surface_score(self, pi_score: float) -> float:
|
||
# 最优速度区间 80-140 m/min（文献[4] 欠酸洗风险判别边界）
|
||
if self.avg_speed < 60:
|
||
speed_score = 80.0
|
||
elif self.avg_speed <= 140:
|
||
speed_score = 80.0 + 15.0 * (self.avg_speed - 60) / 80.0
|
||
else:
|
||
over = (self.avg_speed - 140) / 40.0
|
||
speed_score = 95.0 - 30.0 * over
|
||
return min(max(pi_score * 0.65 + speed_score * 0.35, 0.0), 100.0)
|
||
|
||
def _grade(self, pi: float, surface: float) -> str:
|
||
c = (pi + surface) / 2.0
|
||
if c >= 90: return "A1"
|
||
if c >= 80: return "A2"
|
||
if c >= 70: return "B1"
|
||
if c >= 60: return "B2"
|
||
return "C"
|
||
|
||
def _recommendations(self, pi: float, surface: float) -> List[str]:
|
||
recs = []
|
||
if self.fe_conc_avg > 80:
|
||
recs.append(f"铁离子浓度偏高（{self.fe_conc_avg:.0f} g/L），酸洗能力受抑制，建议加速换酸或补充新酸")
|
||
if pi < 80:
|
||
recs.append("酸洗指数偏低，建议提高酸液浓度至 180 g/L 以上，或将温度升至 80°C")
|
||
if pi < 65:
|
||
recs.append(f"欠酸洗风险高，建议将线速降至 {max(self.avg_speed*0.75, 20):.0f} m/min 以下")
|
||
if self.acid_temp_avg < 70:
|
||
recs.append(f"酸液温度偏低（{self.acid_temp_avg:.1f}°C），建议升温至 75~85°C")
|
||
if self.acid_conc_avg < 120:
|
||
recs.append(f"游离酸浓度偏低（{self.acid_conc_avg:.0f} g/L），建议补充新酸至 150 g/L")
|
||
if self.avg_speed > 150:
|
||
recs.append(f"线速过高（{self.avg_speed:.0f} m/min），欠酸洗风险，建议不超过 140 m/min")
|
||
if self.scale_weight > 12.0:
|
||
recs.append(f"氧化铁皮偏重（{self.scale_weight:.1f} g/m²），建议检查加热炉气氛控制")
|
||
if not recs:
|
||
recs.append("工艺参数在正常范围内，当前设定可继续保持")
|
||
return recs
|
||
|
||
def calculate(self) -> Dict[str, Any]:
|
||
pi = round(self._pickling_index_score(), 1)
|
||
surface = round(self._surface_score(pi), 1)
|
||
return {
|
||
"pi_score": pi,
|
||
"surface_score": surface,
|
||
"overall_grade": self._grade(pi, surface),
|
||
"recommendations": self._recommendations(pi, surface),
|
||
"K_cal": self.K_cal,
|
||
}
|
||
|
||
def calibrate(self, actual_grade: str) -> float:
|
||
"""传入实际质检等级，更新评分校准系数"""
|
||
grade_map = {"A1": 95, "A2": 85, "B1": 75, "B2": 65, "C": 50}
|
||
actual_score = grade_map.get(actual_grade, 75)
|
||
result = self.calculate()
|
||
predicted_score = (result["pi_score"] + result["surface_score"]) / 2.0
|
||
ratio = actual_score / max(predicted_score, 1.0)
|
||
adjustment = 1.0 + 0.3 * (ratio - 1.0)
|
||
adjustment = max(0.7, min(1.3, adjustment))
|
||
self.K_cal = round(self.K_cal * adjustment, 4)
|
||
cal = _load_cal()
|
||
cal[self.CAL_KEY] = self.K_cal
|
||
_save_cal(cal)
|
||
return self.K_cal
|
||
|
||
|
||
# ─────────────────────────────────────────────────────────────────────────────
|
||
# 4. 消耗预测模型
|
||
# ─────────────────────────────────────────────────────────────────────────────
|
||
class AcidConsumptionModel:
|
||
"""
|
||
单卷资源消耗预测。
|
||
单位消耗定额取自浙江企鹅1250mm规格书；
|
||
酸耗额外引入铁离子浓度修正（FeCl₂ 越高酸液越快失效，换酸频率越高）。
|
||
"""
|
||
|
||
ACID_WITH_REGEN = 2.0 # kg/t
|
||
ACID_WITHOUT_REGEN = 35.0 # kg/t
|
||
STEAM_UNIT = 39.8 # kg/t
|
||
POWER_UNIT = 14.0 # kWh/t
|
||
COOLING_UNIT = 1.21 # m³/t
|
||
|
||
def __init__(
|
||
self,
|
||
thickness: float,
|
||
width: float,
|
||
coil_weight_kg: float,
|
||
has_regen_station: bool = True,
|
||
fe_conc_avg: float = 60.0, # FeCl₂ g/L，影响换酸频率
|
||
):
|
||
self.thickness = thickness
|
||
self.width = width
|
||
self.coil_weight_kg = coil_weight_kg
|
||
self.has_regen_station = has_regen_station
|
||
self.fe_conc_avg = fe_conc_avg
|
||
|
||
def calculate(self) -> Dict[str, Any]:
|
||
weight_t = self.coil_weight_kg / 1000.0
|
||
acid_base = self.ACID_WITH_REGEN if self.has_regen_station else self.ACID_WITHOUT_REGEN
|
||
|
||
# 铁离子修正：FeCl₂ > 100 g/L 时酸液利用率下降，有效酸耗上升
|
||
fe_factor = 1.0 + max(0.0, (self.fe_conc_avg - 100.0) / 100.0) * 0.4
|
||
acid_unit = round(acid_base * fe_factor, 3)
|
||
|
||
return {
|
||
"coil_weight_t": round(weight_t, 3),
|
||
"has_regen_station": self.has_regen_station,
|
||
"acid_consumption_kg": round(acid_unit * weight_t, 2),
|
||
"acid_unit_kg_per_t": acid_unit,
|
||
"steam_consumption_kg": round(self.STEAM_UNIT * weight_t, 2),
|
||
"steam_unit_kg_per_t": self.STEAM_UNIT,
|
||
"power_consumption_kwh": round(self.POWER_UNIT * weight_t, 2),
|
||
"power_unit_kwh_per_t": self.POWER_UNIT,
|
||
"cooling_water_m3": round(self.COOLING_UNIT * weight_t, 3),
|
||
"cooling_water_unit_m3_per_t": self.COOLING_UNIT,
|
||
"fe_conc_factor": round(fe_factor, 3),
|
||
}
|