arXiv:2608.00050eess.SPcs.CE2026-08

基于可识别性分析,实现城市尺度污染源精准溯源。

Identifiability-Aware Source Apportionment in City-Scale Advection-Diffusion Systems

  • 用低维非负时序基表示污染源活动,结合风场构建滞后反问题模型。
  • 通过奇异值与相干性评估,确保在噪声下仍能可靠区分污染源。
  • 适用于空气质量监测稀疏的城市场景,尤其适合政策制定者使用。

基于稀疏城市空气质量传感器的污染源解析是受传感器布局、风驱动传输、背景波动和噪声限制的逆问题。已知或代理排放清单通过将未知源场限制为有限候选组,使归因具有意义,但无法保证这些组别可从观测中区分。本文采用低维非负时间基表示时变源活动,将基于清单的溯源建模为风条件下的滞后逆问题,每个源-基系数生成传感器-时间指纹。在剔除独立的低维背景空间后,核心对象为投影后的滞后响应矩阵 $\widetilde H_Φ$:在选定基分辨率下精确可识别需其列满秩,而抗噪归因则由奇异值、系数可见性、背景吸收、成对相干性和射线距离控制。我们提出可识别性感知溯源框架(IASA),用于估计非负源-基系数、重建活动轨迹,并报告不确定性和不可区分源的保守分组建议。在德里平台进行实例化,基于政府提供的PM$_{2.5}$与风速数据、监管传感器位置及四类代理源组,定义了恢复性、模糊性、风多样性、背景压力、传输误差、清单鲁棒性和残差充分性等可控与观测评估指标。IASA报告的是在声明的清单、传输、背景、滞后期和噪声条件下可辩护的溯源分辨率,而非可能达到的最细粒度向量。

原文摘要 · Abstract (English)

Source apportionment from sparse urban air-quality sensors is an inverse problem limited by sensor placement, wind-driven transport, background variation, and noise. Known or proxy emission inventories make attribution meaningful by restricting the unknown source field to a finite set of candidate groups, but do not guarantee those groups are distinguishable from the observations. We represent time-varying source activity with a low-dimensional nonnegative temporal basis and formulate inventory-based apportionment as a wind-conditioned lagged inverse problem in which each source--basis coefficient produces a sensor-time fingerprint. After projecting out a separate low-dimensional background space, the relevant object is the projected lagged response matrix $\widetilde H_Φ$: exact identifiability at the chosen basis resolution requires its full column rank, while noise-robust attribution is controlled by its singular values, coefficient visibility, background absorption, pairwise coherence, and ray distance. We propose an identifiability-aware apportionment (IASA) framework that estimates nonnegative source--basis coefficients, reconstructs activity trajectories, and reports uncertainty and conservative grouping recommendations for indistinguishable sources. We instantiate it on a New Delhi platform built from government PM$_{2.5}$ and wind records, regulatory sensor locations, and four proxy source groups, and define controlled and observed evaluations of recovery, ambiguity, wind diversity, background stress, transport error, inventory robustness, and residual adequacy. IASA reports the attribution resolution defensible under the declared inventories, transport, background, lag, and noise rather than the most detailed possible vector.

污染源解析可识别性城市空气逆问题

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