安全与环境学报

针对低气压环境下气溶胶粒径分布反演的病态问题，提出一种基于Tikhonov正则化改进的松弛算法。通过引入不同阶数的光顺约束项（二阶至四阶），系统比较了正则化松弛法与经典Chahine方法在球形（R-R、L-N分布）及非球形（椭球、圆柱）颗粒反演中的性能。结果表明：四阶光顺法在所有测试场景中均表现最优。对于R-R分布（单峰/双峰/三峰），四阶光顺法反演精度较Chahine方法提升9.84%～24.12%；对于L-N分布，四阶光顺法在0～5.0 μm范围内精度排序第一，而Chahine方法仅在0～1.0 μm超细颗粒反演中优于二阶/三阶光顺。在非球形颗粒反演中，四阶光顺法对椭球与圆柱颗粒的复杂形状表现出良好适应性，1.0%噪声下精度仍保持97.22%。模型验证表明，低气压环境下四阶光顺法的相对均方根误差（RRMSE）为3.8%，显著优于传统算法的5.6%。四阶光顺法因优异的精度与鲁棒性，特别适用于航空器货舱等复杂环境下的火灾探测。

To address the severe ill-posedness of aerosol particle size distribution inversion under low-pressure conditions (10–70 kPa) in aircraft cargo compartments， this study proposes a Tikhonov regularization modified relaxation iterative algorithm. Low-pressure environments enlarge the condition number of the light energy coefficient matrix， reduce measurement signal-to-noise ratio and aggravate the distortion of inversion results; to restrain such oscillation， second-order to fourth-order differential smoothing constraints are embedded into the relaxation iteration framework. The L-curve combined with grid traversal method is adopted to select the optimal regularization parameter λ=10⁻³， balancing data fitting and solution smoothness. Theoretical complexity analysis indicates that the fourth-order smoothing algorithm only brings slight extra single-iteration overhead， while its convergent iteration number drops by 41%， with total runtime below 0.2 s to meet real-time fire detection demands.This paper systematically compares the proposed regularized relaxation methods with classical Chahine algorithm on spherical R-R unimodal/bimodal/trimodal， log-normal (L-N) distributions， as well as non-spherical ellipsoidal and cylindrical particles. Results show that the fourth-order smoothing method outperforms all contrast approaches in all test conditions. For R-R distributions， its inversion accuracy is increased by 9.84%–24.12% compared with Chahine method. Within 0–5.0 μm particle size range of L-N distribution， fourth-order smoothing achieves the highest overall accuracy; only for ultrafine particles of 0–1.0 μm does Chahine perform slightly better than second and third-order smoothing. When 1.0% measurement noise is added， the fourth-order method maintains an inversion accuracy of 97.22% for ellipsoidal and cylindrical particles， showing strong adaptability to irregular particle shapes.A multi-angle light scattering experimental platform with adjustable low-pressure cabin was built for model verification. Under 0.3 atm low-pressure environment， the relative root-mean-square error (RRMSE) of the fourth-order smoothing method is only 3.8%， much lower than the 5.6% error of traditional Chahine algorithm. Despite minor computing cost increment， the fourth-order smoothing regularization relaxation algorithm possesses outstanding anti-noise ability and high reconstruction precision， which can be widely applied to early fire smoke detection in closed low-pressure aircraft cargo compartments. Future work will adopt GPU parallel acceleration to reduce computational overhead and develop hybrid iteration strategies combining Chahine and fourth-order smoothing to further improve inversion efficiency.