发表机构
University of California, Riverside; Bourns College of Engineering（加州大学河滨分校; 伯恩工程学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出多尺度可见性理论，通过复合算子行空间度量任务可访问性，统一保留、鲁棒性与可检测性，并经合成基准验证，在弱任务与强干扰下实现精确的决策可见性。
AI 中文摘要
多尺度可见性理论（MVT）被提出作为一种任务相对的算子几何框架，用于确定规定信息如何在结构化观测架构中存续并保持可访问性。该理论并非仅通过变换幅度、输出能量、秩或信号显著性来评估观测质量，而是通过复合算子 A_A = R_E W_rho H_beta P_Omega 的行空间来衡量指定任务方向或任务子空间的可访问性。与基于投影的、聚焦于标称系统行为与故障相关系统行为之间区分的诊断框架不同，MVT 在观测架构、尺度、表示和保留访问发生变化时，追踪一个独立规定的任务。该公式统一了精确的分阶段保留、任务子空间保持、尺度索引的可见性与稳定性、最坏情况擦除鲁棒性、集体可见性、协方差归一化统计分离以及决策充分性，同时保持几何可访问性、统计可检测性和决策充分性在数学上的区分。一个可复现的 MATLAB 实现通过一个受控合成基准验证了分析关系，该基准包含一个弱的 260 Hz 规定任务和一个较强的 380 Hz 干扰。在同一频率索引的观测族内，任务可见性在 260 Hz 处最大化，而完整信号观测能量在 380 Hz 处最大化。在标称噪声水平下，D_max = 18 > Gamma_D = 8.563847350668，产生 258.5-261.5 Hz 的决策可见区间。一个四行相位冗余观测器在两次行擦除后仍保持完整的任务模型可见性，而两个分别低于阈值的 258 Hz 和 262 Hz 分支通过 D_12 = 10.470833520729 联合变得决策可见。所有 12 项数值审计均满足 10^-10 的容差。
英文摘要
Multiscale Visibility Theory (MVT) is introduced as a task-relative operator-geometric framework for determining how prescribed information survives and remains accessible through a structured observation architecture. Rather than evaluating observation quality by transform magnitude, output energy, rank, or signal prominence alone, MVT measures the accessibility of a specified task direction or task subspace through the row space of the composite operator A_A = R_E W_rho H_beta P_Omega. Unlike projection-based diagnostic frameworks centered on discrimination between nominal and fault-related system behavior, MVT tracks an independently prescribed task as observation architecture, scale, representation, and retained access vary. The formulation unifies exact stagewise retention, task-subspace preservation, scale-indexed visibility and stability, worst-case erasure robustness, collective visibility, covariance-normalized statistical separation, and decision sufficiency while keeping geometric accessibility, statistical detectability, and decision adequacy mathematically distinct. A reproducible MATLAB implementation verifies the analytical relations using a controlled synthetic benchmark with a weak 260-Hz prescribed task and a stronger 380-Hz nuisance. Within the same frequency-indexed observation family, task visibility is maximized at 260 Hz, whereas complete-signal observation energy is maximized at 380 Hz. At the nominal noise level, D_max = 18 > Gamma_D = 8.563847350668, yielding a decision-visible interval of 258.5-261.5 Hz. A four-row phase-redundant observer preserves full task-model visibility through two row erasures, while two individually subthreshold branches at 258 and 262 Hz become jointly decision-visible with D_12 = 10.470833520729. All 12 numerical audits satisfy the 10^-10 tolerance.
