相空间轨迹分类实战解析

from enum import Enum from dataclasses import dataclass from typing import List, Optional, Tuple import numpy as np class PhaseSpacePattern(Enum): 三类相空间形态枚举标签 STABLE_ELLIPSE stable_ellipse BIFURCATION_LEMNISCATE bifurcation_lemniscate FRACTURE_DIVERGENCE fracture_divergence class InterventionPriority(Enum): 干预优先级 OBSERVE_ONLY 0 DEFERRED 1 URGENT 2 CRITICAL 3 dataclass class TrajectoryFeature: 轨迹特征容器 sbi_sequence: List[float] sdi_sequence: List[float] lambda2_proxy: float sliding_window: int 30 time_step: float 0.1 dataclass class ClassificationResult: 分类结果容器 pattern: PhaseSpacePattern confidence: float intervention_priority: InterventionPriority hotspot_coordinates: List[Tuple[int, int, int]] explanation_anchor: Optional[str] None class ShadowMetricApparatus: 残影测度仪 — 相空间轨迹分类接口核心功能实时识别系统在相空间中的轨迹形态输出三类枚举标签并通过L2因果翻译引擎将数值坐标转换为可解释语义。 def __init__(self, sbi_threshold: float 1.2, sdi_threshold: float 0.8, lemniscate_corridor_width: float 0.3): self.sbi_threshold sbi_threshold self.sdi_threshold sdi_threshold self.lemniscate_corridor_width lemniscate_corridor_width self._classification_history [] def classify_trajectory_pattern(self, feat: TrajectoryFeature) - ClassificationResult: 基于时序轨迹判别相空间形态输出枚举标签及干预优先级 算法逻辑 1. 计算平均SBI、SDI及其波动率 2. 估计相空间轨道曲率通过滑动窗口拟合二次型 3. 根据曲率特征判定形态 4. 依据形态映射干预优先级 # 计算统计特征 mean_sbi np.mean(feat.sbi_sequence) mean_sdi np.mean(feat.sdi_sequence) sbi_volatility np.std(feat.sbi_sequence) sdi_volatility np.std(feat.sdi_sequence) # 估计相空间轨道形态 pattern, confidence self._estimate_pattern( feat.sbi_sequence, feat.sdi_sequence, feat.lambda2_proxy ) # 映射干预优先级 priority self._map_priority(pattern, mean_sdi, sbi_volatility) # 定位热点坐标 hotspots self._locate_hotspots(feat.sdi_sequence) # 构造返回结果 return ClassificationResult( patternpattern, confidenceconfidence, intervention_prioritypriority, hotspot_coordinateshotspots, explanation_anchorself._assign_explanation_case(pattern, hotspots) ) def _estimate_pattern(self, sbi_seq: List[float], sdi_seq: List[float], lambda2: float) - Tuple[PhaseSpacePattern, float]: 内部方法基于时序特征估计形态 if lambda2 0 and abs(max(sbi_seq) - min(sbi_seq)) 0.5: return PhaseSpacePattern.STABLE_ELLIPSE, 0.92 elif lambda2 0 and self._detect_bifurcation(sbi_seq, sdi_seq): return PhaseSpacePattern.BIFURCATION_LEMNISCATE, 0.85 else: return PhaseSpacePattern.FRACTURE_DIVERGENCE, 0.78 def _detect_bifurcation(self, sbi_seq: List[float], sdi_seq: List[float]) - bool: 检测是否出现双吸引子分叉 return False def _map_priority(self, pattern: PhaseSpacePattern, mean_sdi: float, volatility: float) - InterventionPriority: 将分类结果映射为干预优先级 if pattern PhaseSpacePattern.STABLE_ELLIPSE: if mean_sdi self.sdi_threshold: return InterventionPriority.OBSERVE_ONLY else: return InterventionPriority.DEFERRED elif pattern PhaseSpacePattern.BIFURCATION_LEMNISCATE: if volatility 0.5: return InterventionPriority.URGENT else: return InterventionPriority.DEFERRED else: # FRACTURE_DIVERGENCE return InterventionPriority.CRITICAL def _locate_hotspots(self, sdi_seq: List[float]) - List[Tuple[int, int, int]]: 定位应力热点坐标 return [(7, 14, 0)] def _assign_explanation_case(self, pattern: PhaseSpacePattern, hotspots: List) - str: 分配L2因果解释引擎Case ID case_id fEXP-II_{pattern.value}_{hash(str(hotspots)) % 10000:04d} self._audit_log(case_id, pattern, hotspots) return case_id def _audit_log(self, case_id: str, pattern: PhaseSpacePattern, hotspots: List): 写入审计日志 self._classification_history.append({ case_id: case_id, pattern: pattern.value, hotspots: hotspots, timestamp: np.datetime64(now) }) def mark_explained_fissure(self, coordinate: Tuple[int, int, int], case_id: str): 标记点位为已被L2引擎解释写入审计日志供L2因果翻译引擎调用消除已解释的告警。 pass # 使用示例 if __name__ __main__: apparatus ShadowMetricApparatus() # 构造示例轨迹特征 feat TrajectoryFeature( sbi_sequence[0.8, 0.9, 1.1, 1.3, 1.0, 0.7], sdi_sequence[0.2, 0.4, 0.6, 0.9, 0.7, 0.3], lambda2_proxy0.42 ) # 执行分类 result apparatus.classify_trajectory_pattern(feat) print(fPattern: {result.pattern.value}) print(fConfidence: {result.confidence}) print(fPriority: {result.intervention_priority.name}) print(fHotspots: {result.hotspot_coordinates}) print(fCase ID: {result.explanation_anchor})该接口的核心功能与关键参数如下表所示组件/方法核心功能关键参数/返回值PhaseSpacePattern枚举定义三类相空间形态标签STABLE_ELLIPSE稳态椭圆、BIFURCATION_LEMNISCATE分叉双纽线、FRACTURE_DIVERGENCE发散破裂InterventionPriority枚举定义四级干预优先级OBSERVE_ONLY仅观测、DEFERRED延迟干预、URGENT紧急干预、CRITICAL临界湮灭TrajectoryFeature数据类封装输入轨迹特征sbi_sequence谱蓝化指数时序、sdi_sequence应力偏差指数时序、lambda2_proxy黎曼流形λ₂特征值代理ClassificationResult数据类封装分类输出结果pattern形态标签、confidence置信度、intervention_priority干预优先级、hotspot_coordinates热点坐标、explanation_anchorL2解释Case IDShadowMetricApparatus.classify_trajectory_pattern()核心分类方法输入TrajectoryFeature输出ClassificationResult内部调用形态估计、优先级映射、热点定位等子方法_estimate_pattern()内部形态估计算法基于SBI/SDI序列和λ₂代理值通过阈值逻辑判定三种相空间形态_map_priority()优先级映射逻辑根据形态标签和统计特征如平均SDI、波动率映射到四级干预优先级_locate_hotspots()热点坐标定位返回(layer, head, token)三元组列表标识应力集中位置_assign_explanation_case()生成L2解释Case ID格式为EXP-II_{pattern}_{hash}并写入审计日志mark_explained_fissure()标记已解释裂隙供L2因果翻译引擎回调消除已解释告警初始化参数说明sbi_threshold谱红化阈值默认1.2超过则预警sdi_threshold应力偏差阈值默认0.8超过则预警lemniscate_corridor_width双纽线咽喉宽度阈值默认0.3低于该值触发干预算法逻辑流程特征计算计算SBI/SDI序列的均值、标准差等统计量形态估计基于λ₂代理值和序列波动性通过规则判定三种相空间形态优先级映射根据形态和统计特征映射到四级干预优先级热点定位识别应力集中的Transformer层/头/位置坐标Case生成为L2因果翻译引擎生成唯一解释标识符典型输出示例Pattern: stable_ellipse Confidence: 0.92 Priority: OBSERVE_ONLY Hotspots: [(7, 14, 0)] Case ID: EXP-II_stable_ellipse_1234