基于PLE网络的电加热防冰功率分布优化设计

doi:10.7527/S1000-6893.2025.32179

Abstract

Abstract:

Electrothermal anti-icing systems are one of the key technologies for preventing aircraft icing and ensuring flight safety， with their anti-icing efficiency being directly influenced by the power distribution of heating elements. Research on the optimal design of such systems is of great significance for reducing energy consumption and enhancing system safety. To address the limitations of traditional power distribution optimization—namely， the requirement of repeated numerical simulations of steady-state ice accretion， water film， and temperature distributions， which result in high computational cost and low optimization efficiency—this study proposes an optimized power distribution design method for electrothermal anti-icing systems based on an improved Progressive Layered Extraction （PLE） network. A multi-task learning framework is constructed by employing Proper Orthogonal Decomposition （POD） to reduce the dimensionality of numerical simulation data， including water film， ice accretion， and temperature distributions on the wing surface. The power distribution parameters are used as inputs， and the POD modal coefficients as outputs. Based on the PLE architecture， the network is enhanced by explicitly integrating task-specific expert information into the gating mechanism and introducing an attention mechanism at the shared expert output， thereby improving the model’s capability to extract task-relevant features. Experimental results demonstrate that the improved multi-task learning model achieves high accuracy across all three prediction tasks， with root mean square errors of 0.045 8 for water film， 0.084 8 for ice accretion， and 0.714 9 for temperature on the test set. Finally， a single-objective optimization of the power distribution is performed using a genetic algorithm， aiming to minimize total power consumption under a set of physical constraints. Compared to the reference scheme， the optimized power distribution achieves approximately 34.3% reduction in energy consumption. Numerical simulation results further verify that the optimized scheme meets anti-icing requirements while significantly reducing power demand.

Key words: electrothermal anti-icing system, wing, optimization design, improved PLE network, proper orthogonal decomposition

CLC Number:

Haiyang TANG, Zhefan REN, Ningli CHEN, Xian YI, Zhiyong CHEN. Optimization design of electrothermal anti-icing power distribution based on PLE network[J]. Acta Aeronautica et Astronautica Sinica, 2026, 47(2): 132179.

Figures/Tables 18

Fig.1

Fig.2

Fig.3

Table 1

Heating element area and operating parameter range

加热区域	坐标区间/m	参数取值范围/（kW·m^-2）	对应面积/（10^-3 m²）
$A$	（-0.004 1，0.012 4）	［0，50］	5.570
$B$	（-0.021 3，-0.004 6）	［0，50］	7.630
$C$	（0.012 8，0.025 6）	［0，50］	7.853
$D$	（-0.031 2，-0.021 7）	［0，50］	7.529
$E$	（0.026 0， 0.033 7）	［0，50］	7.574
$F$	（-0.040 1，-0.031 7）	［0，50］	11.731
$G$	（0.034 1，0.042 0）	［0，50］	11.182

Table 1

Table 2

Calculation of working conditions

参数	取值
来流温度T₀/K	251.15
来流速度v/（m·s^-1）	89.408
水滴平均体积直径 $D m v / μ m$	20
液态水含量 $C l w /$ （g·m^-3）	0.31
压强p/MPa	0.1

Table 2

Fig.4

Fig.5

Fig.6

Fig. 7

Table 3

Table 4

Fig.8

Fig.9

Fig.10

Table 5

Model evaluation metrics

模型	结冰厚度误差/m		水膜厚度误差/m		温度误差/K
模型	$E r m s$	$E m a$	$E r m s$	$E m a$	$E r m s$	$E m a$
设计1	0.052 6	0.013 9	0.113 9	0.038 1	1.124 0	0.557 1
设计2	0.058 5	0.015 4	0.136 6	0.051 3	1.035 4	0.471 9
设计3	0.047 5	0.011 3	0.092 2	0.031 7	0.865 5	0.390 1
设计4	0.046 3	0.010 8	0.085 9	0.030 3	0.760 2	0.343 3
设计5	0.046 2	0.010 6	0.087 4	0.029 4	0.745 1	0.332 7
本文框架	0.045 8	0.010 7	0.084 8	0.029 6	0.714 9	0.326 9

Table 5

Fig.11

Table 6

Comparison of results from three optimizations

优化次序	$Q A$ /（kW·m^-2）	$Q B$ /（kW·m^-2）	$Q C$ /（kW·m^-2）	$Q D$ /（kW·m^-2）	$Q E$ /（kW·m^-2）	$Q F$ /（kW·m^-2）	$Q G$ /（kW·m^-2）	P_total/kW
优化#1	8.172	13.727	29.111	27.859	5.364	13.460	14.570	0.950 0
优化#2	6.738	17.159	27.605	24.924	11.431	12.421	15.752	0.981 4
优化#3	18.093	26.149	13.488	12.359	15.173	15.675	18.389	1.003 7

Table 6

Fig.12

References 33

[1]	ZHANG Y， ZHANG Y， LUO G， et al. Research progress of aircraft icing hazard and ice wind tunnel test technology［EB/OL］. ［2025-03-05］. .
[2]	LYNCH F T， KHODADOUST A. Effects of ice accretions on aircraft aerodynamics［J］. Progress in Aerospace Sciences， 2001， 37（8）： 669-767.
[3]	APPIAH-KUBP. U.S. inflight icing accidents and incidents， 2006 to 2010［D］. Knoxville： The University of Tennessee， 2013.
[4]	刘欣乐，姜亚楠，辛荣提，等. 超疏水电热复合分区防冰策略［J］. 航空学报， 2025， 46（9）： 155-165.
	LIU X L， JIANG Y N， XIN R T， et al. Anti-icing stra-tegy of superhydrophobic electric thermal composite zo-ning［J］. Acta Aeronautica et Astronautica Sinica， 2025， 46（9）： 155-165 （in Chinese）.
[5]	SILVA G， SILVARES O， ZERBINI E. Airfoil anti-ice system modeling and simulation［C］∥41st Aerospace Sciences Meeting and Exhibit. Reston： AIAA， 2003.
[6]	苏媛，徐忠达，吴祯龙. 飞机积冰后若干飞行力学问题综述［J］. 航空动力学报， 2014， 29（8）： 1878-1893.
	SU Y， XU Z D， WU Z L. Overview of several ice accretion effects on aircraft flight dynamics［J］. Journal of Aerospace Power， 2014， 29（8）： 1878-1893 （in Chinese）.
[7]	WU Y N， ZHANG D L， CHEN W J， et al. Optimization for electric heating power’s distribution on electro-thermal anti-icing surface［C］∥CSAA/IET International Conference on Aircraft Utility Systems. Guiyang： CSAA， 2019： 779-784.
[8]	ARIZMENDI GUTIÉRREZ B， DELLA NOCE A， GALLIA M， et al. Optimization of a thermal ice protection system by means of a genetic algorithm［M］∥Bioinspired optimization methods and their applications. Cham： Springer International Publishing， 2020： 189-200.
[9]	刘宗辉，卜雪琴，林贵平，等. 基于PHengLEI的非稳态电热除冰过程仿真［J］. 空气动力学学报， 2023， 41（2）： 53-63.
	LIU Z H， BU X Q， LIN G P， et al. Simulation of unsteady electrothermal deicing process based on PHengLEI［J］. Acta Aerodynamica Sinica， 2023， 41（2）： 53-63 （in Chinese）.
[10]	GUO X F， YANG Q， ZHENG H R， et al. Optimization of power distribution for electrothermal anti-icing systems by differential evolution algorithm［J］. Applied Thermal Engineering， 2023， 221： 119875.
[11]	POURBAGIAN M， HABASHI W G. Surrogate-based optimization of electrothermal wing anti-icing systems［J］. Journal of Aircraft， 2013， 50（5）： 1555-1563.
[12]	POURBAGIAN M， HABASHI W. Power and design optimization of electro-thermal anti-icing systems via FENSAP-ICE［C］∥The 4th AIAA Atmospheric and Space Environments Conference. Reston： AIAA， 2012.
[13]	NIU J， SANG W， QIU A， et al. An optimization of anti-icing chamber based on POD and Kriging［EB/OL］. ［2025-04-29］. .
[14]	杨倩，郑皓冉，程显达，等. 基于引气控制的热气防冰优化设计方法［J］. 航空学报， 2023， 44（S2）： 729285.
	YANG Q， ZHENG H R， CHENG X D， et al. Optimization design method for hot air anti-icing system based on bleed air control［J］. Acta Aeronautica et Astronautica Sinica， 2023， 44（S2）： 729285 （in Chinese）.
[15]	杨倩，郭晓峰，李芹，等. 基于POD和代理模型的热气防冰性能预测方法［J］. 航空学报， 2023， 44（1）： 626992.
	YANG Q， GUO X F， LI Q， et al. Hot air anti-icing performance estimation method based on POD and surrogate model［J］. Acta Aeronautica et Astronautica Sinica， 2023， 44（1）： 626992 （in Chinese）.
[16]	柳家齐，陈荣钱，楼锦华，等. 基于深度学习的高速直升机旋翼翼型气动优化设计［J］. 航空学报， 2024， 45（9）： 529828.
	LIU J Q， CHEN R Q， LOU J H， et al. Aerodynamic shape optimization of high-speed helicopter rotor airfoil based on deep learning［J］. Acta Aeronautica et Astronautica Sinica， 2024， 45（9）： 529828 （in Chinese）.
[17]	LIU J， KE P. Aero-engine inlet vane structure optimization for anti-icing with hot air film using neural network and genetic algorithm： 2019-01-2021［EB/OL］. ［2025-02-05］. .
[18]	屈经国，彭博，易贤，等. 基于深度神经网络的任意翼型结冰预测方法［J］. 空气动力学学报， 2023， 41（7）： 48-55.
	QU J G， PENG B， YI X， et al. Icing prediction method for arbitrary airfoil using deep neural networks［J］. Acta Aerodynamica Sinica， 2023， 41（7）： 48-55 （in Chinese）.
[19]	何磊，钱炜祺，易贤，等. 基于转置卷积神经网络的翼型结冰冰形图像化预测方法［J］. 国防科技大学学报， 2021， 43（3）： 98-106.
	HE L， QIAN W Q， YI X， et al. Graphical prediction method of airfoil ice shape based on transposed convolution neural networks［J］. Journal of National University of Defense Technology， 2021， 43（3）： 98-106 （in Chinese）.
[20]	WANG X， KOU J Q， ZHANG W W. Unsteady aerodynamic prediction for iced airfoil based on multi-task lear-ning［J］. Physics of Fluids， 2022， 34（8）： 087117.
[21]	陈宁立，易贤，王强，等. NNW-ICE软件的三维结冰模型及精度验证［J］. 航空学报， 2024， 45（12）： 129188.
	CHEN N L， YI X， WANG Q， et al. Three-dimensional model for ice accretion in NNW-ICE software and validation of its precision［J］. Acta Aeronautica et Astronautica Sinica， 2024， 45（12）： 129188 （in Chinese）.
[22]	CHEN N L， YI X， WANG Q， et al. Numerical study on wind-driven thin water film runback on an airfoil［J］. AIAA Journal， 2023， 61（6）： 2517-2525.
[23]	CHEN N L， YI X， WANG Q， et al. An analysis of heat transfer inside the ice layer and solid wall during ice accretion［J］. International Communications in Heat and Mass Transfer， 2022， 137： 106276.
[24]	ROWLEY C W. Model reduction for fluids， using ba-lanced proper orthogonal decomposition［J］. International Journal of Bifurcation and Chaos， 2005， 15（3）： 997-1013.
[25]	BERKOOZ G， HOLMES P， LUMLEY J L. The proper orthogonal decomposition in the analysis of turbulent flows［J］. Annual Review of Fluid Mechanics， 1993， 25： 539-575.
[26]	张钰，刘建伟，左信. 多任务学习［J］. 计算机学报， 2020， 43（7）： 1340-1378.
	ZHANG Y， LIU J W， ZUO X. Survey of multi-task learning［J］. Chinese Journal of Computers， 2020， 43（7）： 1340-1378 （in Chinese）.
[27]	ZHANG Y， YANG Q. A survey on multi-task learning［J］. IEEE Transactions on Knowledge and Data Engineering， 2022， 34（12）： 5586-5609.
[28]	VASWANI A， SHAZEER N， PARMAR N， et al. Attention is all you need［DB/OL］. arXiv preprint： 1706.03762， 2024.
[29]	MISRA I， SHRIVASTAVA A， GUPTA A， et al. Cross-stitch networks for multi-task learning［EB/OL］. ［2025-02-05］. .
[30]	TANG H Y， LIU J N， ZHAO M， et al. Progressive layered extraction （PLE）： A novel multi-task learning （MTL） model for personalized recommendations［C］∥Fourteenth ACM Conference on Recommender Systems. New York： ACM， 2020： 269-278.
[31]	赵志鹏. 基于改进深度多任务学习的滚动轴承故障预测方法研究［D］. 成都：电子科技大学， 2023.
	ZHAO Z P. Research on rolling bearing fault prediction method based on improved deep multi-task learning［D］. Chengdu： University of Electronic Science and Techno-logy of China， 2023 （in Chinese）.
[32]	张大海，孙锴，倪平浩. 基于耦合关系挖掘及渐进式分层提取多任务学习网络的风-光-荷短期预测［J］. 电网技术， 2023， 47（9）： 3537-3547.
	ZHANG D H， SUN K， NI P H. Wind-photovoltaic-load short-term forecast based on coupling relation mining and progressive layered extraction of multi-task lear-ning network［J］. Power System Technology， 2023， 47（9）： 3537-3547 （in Chinese）.
[33]	MORENCY F， TEZOK F， PARASCHIVOIU I. Anti-icing system simulation using CANICE［J］. Journal of Aircraft， 1999， 36（6）： 999-1006.

网络参数	设置
专家网络类型	深度神经网络（DNN）
独有专家网络数	6
共享专家网络数	3
专家网络隐藏层	4
特征提取层层数	2

序号	Q_A/（kW·m^-2）	Q_B/（kW·m^-2）	Q_C/（kW·m^-2）	Q_D/（kW·m^-2）	Q_E/（kW·m^-2）	Q_F/（kW·m^-2）	Q_G/（kW·m^-2）
1	40.435	34.875	42.395	47.855	6.785	38.675	28.525
2	33.235	48.245	0.895	45.655	9.375	34.215	28.675
3	16.275	3.395	35.805	22.375	28.675	17.145	22.395
850	11.795	19.045	27.545	42.485	3.785	30.215	5.395

Optimization design of electrothermal anti-icing power distribution based on PLE network

RichHTML

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

Figures/Tables 18

References 33

Related Articles 15

Recommended Articles

Metrics

Comments

[1]	Kai CUI, Zesen WANG, Yao XIAO, Zhongwei TIAN, Guangli LI, Siyuan CHANG. A novel wide-speed-range configuration based on high-pressure capturing wing concept and its transonic aerodynamic characteristics [J]. Acta Aeronautica et Astronautica Sinica, 2026, 47(1): 632102-632102.
[2]	Yang ZHANG, Zhonghua HAN, Keshi ZHANG, Ke SONG, Wenping SONG. Aerodynamic design optimization of hypersonic vehicles considering lift matching [J]. Acta Aeronautica et Astronautica Sinica, 2026, 47(1): 632064-632064.
[3]	Tielin MA, Biao JING, Chongwen JIANG, Nanxuan QIAO, Jingcheng FU, Jinwu XIANG. Configuration design and mission capability evaluation of a cross-speed-range waverider-integrated morphing wing [J]. Acta Aeronautica et Astronautica Sinica, 2026, 47(1): 632051-632051.
[4]	Xiayang ZHANG, Bin LUO, Xi CHEN, Tao YANG. Optimization design of high-efficiency and low-noise rotor layout for quad-tiltrotor aircraft [J]. Acta Aeronautica et Astronautica Sinica, 2025, 46(S1): 732183-732183.
[5]	Pengqian YANG, Yutong CHEN, Junhui LIU, Jiehao YANG, Jiayuan SHAN, Shijun SUN. Aerodynamic and operational characteristics analysis for tandem wing cargo UAV at high angle of attack [J]. Acta Aeronautica et Astronautica Sinica, 2025, 46(9): 131056-131056.
[6]	Kelei WANG, Zhou ZHOU, Minghao LI. Research and experimental validation of loose coupling design method for propulsion wing unit [J]. Acta Aeronautica et Astronautica Sinica, 2025, 46(9): 212-229.
[7]	Feng LIU, Sen YANG, Zhenpeng WEI. Variable chord wing based on composite material elastic periodic structure and pre-stressed skin [J]. Acta Aeronautica et Astronautica Sinica, 2025, 46(7): 230966-230966.
[8]	Yihao XU, Pengcheng DONG, Junchao ZHENG, Chunqing TAN, Hailong TANG. Overall performance optimization method of adaptive cycle propulsion system [J]. Acta Aeronautica et Astronautica Sinica, 2025, 46(7): 130987-130987.
[9]	Yifan YANG, Xiao WANG. Enhanced hybrid vortex particle method for aerodynamic analysis of tiltrotor rotor/wing interactions [J]. Acta Aeronautica et Astronautica Sinica, 2025, 46(7): 131040-131040.
[10]	Guocheng YAN, Honglun WANG, Yanxiang WANG, Yuebin LUN, Junfan ZHU. Prescribed performance anti-swing control for wing rotation process of UAV towed aerial recovery [J]. Acta Aeronautica et Astronautica Sinica, 2025, 46(24): 331840-331840.
[11]	Anping ZHANG, Hao DONG. UAV swarms and their takeoff method for high-end warfare [J]. Acta Aeronautica et Astronautica Sinica, 2025, 46(22): 331034-331034.
[12]	Luofeng WANG, Renliang CHEN, Rui FENG. Cross-medium rigid-flexible coupled modeling and trim analysis of helicopter mine-clearing system [J]. Acta Aeronautica et Astronautica Sinica, 2025, 46(22): 231900-231900.
[13]	Chao YAN, Zexu ZHANG, Hutao CUI, Kai ZHANG, Jingzong LIU. Predefined-time affine formation maneuvering control for fixed-wing UAV swarm [J]. Acta Aeronautica et Astronautica Sinica, 2025, 46(22): 331824-331824.
[14]	Yan WANG, Liang CHEN, Yongming CAI, Lilong LUO. Optimization method for primary load-bearing structure of blended wing body aircraft using reduced-dimensional models [J]. Acta Aeronautica et Astronautica Sinica, 2025, 46(21): 532406-532406.
[15]	Yanjie LIU, Mingqiang LI, Xuan GUO, Yanfei SU, Bintuan WANG, Yingju XUE. Optimization design of high-load-bearing opening structures in special configuration aircraft [J]. Acta Aeronautica et Astronautica Sinica, 2025, 46(21): 532447-532447.