Representation of combustion thermochemical manifolds via multi-gate mixture of experts

doi:10.3785/j.issn.1008-973X.2023.12.007

Journal of ZheJiang University (Engineering Science)

2023, Vol. 57

Issue (12): 2401-2411 DOI: 10.3785/j.issn.1008-973X.2023.12.007

Representation of combustion thermochemical manifolds via multi-gate mixture of experts

Yi-cun WANG1(

),Chang-xiao SHAO2,Tai JIN3,Jiang-kuan XING1,Kun LUO1,4,*(

),Jian-ren FAN1,4

1. State Key Laboratory of Clean Energy Utilization, Zhejiang University, Hangzhou 310027, China
2. Center for Turbulence Control, Harbin Institute of Technology, Shenzhen Campus, Shenzhen 518055, China
3. School of Aeronautics and Astronautics, Zhejiang University, Hangzhou 310027, China
4. Shanghai Institute for Advanced Study of Zhejiang University, Shanghai 200120, China

Download:

HTML

PDF(2887KB) HTML
Export: BibTeX | EndNote (RIS)

Abstract

The multi-gate mixture of experts (MMoE) for multi-task learning was applied to better implement the representation of combustion thermochemical manifolds in the framework of flamelet-based combustion models. Detailed chemistry (DC) simulation of a three-dimensional laminar spray jet flame was conducted to generate the original dataset. The original dataset was preprocessed by Box-Cox transformation and Z-score normalization to deal with the multi-scale distributions of combustion data. Correlation analysis was performed on the dataset using the Pearson correlation coefficient, and the results showed that there was no significant correlation between some chemical species. The MMoE and feedforward neural network (FNN) models were constructed respectively, and the comparison and analysis showed that although both models achieved similar loss values and coefficients of determination, the MMoE model was more stable during the training process and achieved more accurate quantitative prediction results than FNN model.

Key words： multi-gate mixture of experts (MMoE) feedforward neural network (FNN) flamelet model laminar spray flame numerical simulation of combustion

Received: 15 April 2023 Published: 27 December 2023

CLC:

TK 4

Fund: 国家杰出青年科学基金资助项目（51925603）；国家自然科学基金资助项目（52236002）

Corresponding Authors: Kun LUO E-mail: wangyicun@zju.edu.cn;zjulk@zju.edu.cn

	Service
	E-mail this article
	Add to my bookshelf
	Add to citation manager
	E-mail Alert
	RSS
	Articles by authors
	Yi-cun WANG
	Chang-xiao SHAO
	Tai JIN
	Jiang-kuan XING
	Kun LUO
	Jian-ren FAN

Cite this article:

Yi-cun WANG,Chang-xiao SHAO,Tai JIN,Jiang-kuan XING,Kun LUO,Jian-ren FAN. Representation of combustion thermochemical manifolds via multi-gate mixture of experts. Journal of ZheJiang University (Engineering Science), 2023, 57(12): 2401-2411.

URL:

https://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2023.12.007 OR https://www.zjujournals.com/eng/Y2023/V57/I12/2401

基于多门控混合专家网络的燃烧热化学流形表征

为了更好地在小火焰燃烧模型框架内实施燃烧热化学流形表征，采用多任务学习领域中的多门控混合专家网络（MMoE）. 通过对三维层流喷雾射流火焰构型进行详细化学（DC）模拟，构建原始数据集. 原始数据集经过Box-Cox转换和标准化处理，以应对燃烧数据的多尺度分布问题. 对数据集进行Pearson相关系数分析，结果表明部分化学组分之间无明显的相关性. 分别构建同等参数量规模的MMoE和前馈神经网络（FNN）模型，对比分析结果表明，2种模型取得的损失值和决定系数相近，但相比FNN模型，MMoE模型在训练过程中更加稳定，且取得的定量预测结果更加准确.

关键词： 多门控混合专家网络 (MMoE), 前馈神经网络（FNN）, 小火焰模型, 层流喷雾火焰, 燃烧数值模拟

Fig.1 Schematic of configuration of spray jet flame

Tab.1 Inflow parameters of spray jet flame

Fig.2 Schematic of neural network

Tab.2 Structure of expert network and tower network in multi-gate mixture of experts

Fig.3 Contour plots of thermochemical quantities

Fig.4 Heatmap of correlation coefficients for different species

Tab.3 Final loss values for different neural network models

Fig.5 Loss values versus iterations for different neural networks

Fig.6 Scatter plots of true and predicted values using FNN model

Fig.7 Scatter plots of true and predicted values using MMoE model

Tab.4 Coefficients of determination for FNN and MMoE models

Fig.8 Comparisons of detailed chemistry results and solutions using different neural networks at axial location of x/D = 15

Fig.9 Comparisons of detailed chemistry results and solutions using different neural networks at axial location of x/D = 25

Fig.10 Comparisons of detailed chemistry results and solutions using different neural networks at axial location of x/D = 30

Fig.11 Contour plots of gas temperature for mew case

Tab.5 Final loss values of different neural network for new case

Fig.12 Loss values versus iterations of different neural networks for new case


[1]	KARNIADAKIS G E, KEVREKIDIS I G, LU L, et al Physics-informed machine learning[J]. Nature Reviews Physics, 2021, 3 (6): 422- 440 doi: 10.1038/s42254-021-00314-5

[2]	ZHOU L, SONG Y, JI W, et al Machine learning for combustion[J]. Energy and AI, 2022, 7: 100128 doi: 10.1016/j.egyai.2021.100128

[3]	IHME M, CHUNG W T, MISHRA A A Combustion machine learning: principles, progress and prospects[J]. Progress in Energy and Combustion Science, 2022, 91: 101010 doi: 10.1016/j.pecs.2022.101010

[4]	ZHU L T, CHEN X Z, BO O, et al Review of machine learning for hydrodynamics, transport, and reactions in multiphase flows and reactors[J]. Industrial and Engineering Chemistry Research, 2022, 61 (28): 9901- 9949 doi: 10.1021/acs.iecr.2c01036

[5]	POPE S B Computationally efficient implementation of combustion chemistry using in situ adaptive tabulation[J]. Combustion Theory and Modelling, 1997, 1 (1): 41- 63 doi: 10.1080/713665229

[6]	TONSE S R, MORIARTY N W, BROWN N J, et al PRISM: piecewise reusable implementation of solution mapping. An economical strategy for chemical kinetics[J]. Israel Journal of Chemistry, 1999, 39 (1): 97- 106 doi: 10.1002/ijch.199900010

[7]	IHME M, SEE Y C Prediction of autoignition in a lifted methane/air flame using an unsteady flamelet/progress variable model[J]. Combustion and Flame, 2010, 157 (10): 1850- 1862 doi: 10.1016/j.combustflame.2010.07.015

[8]	ZHANG Y, XU S, ZHONG S, et al Large eddy simulation of spray combustion using flamelet generated manifolds combined with artificial neural networks[J]. Energy and AI, 2020, 2: 100021 doi: 10.1016/j.egyai.2020.100021

[9]	KEMPF A, FLEMMING F, JANICKA J Investigation of lengthscales, scalar dissipation, and flame orientation in a piloted diffusion flame by LES[J]. Proceedings of the Combustion Institute, 2005, 30: 557- 565 doi: 10.1016/j.proci.2004.08.182

[10]	CHATZOPOULOS A K, RIGOPOULOS S A chemistry tabulation approach via rate-controlled constrained equilibrium (RCCE) and artificial neural networks (ANNs), with application to turbulent non-premixed CH4/H2/N2 flames [J]. Proceedings of the Combustion Institute, 2013, 34: 1465- 1473 doi: 10.1016/j.proci.2012.06.057

[11]	ZHANG T, YI Y, XU Y, et al A multi-scale sampling method for accurate and robust deep neural network to predict combustion chemical kinetics[J]. Combustion and Flame, 2022, 245: 112319 doi: 10.1016/j.combustflame.2022.112319

[12]	AN J, HE G, LUO K, et al Artificial neural network based chemical mechanisms for computationally efficient modeling of hydrogen/carbon monoxide/kerosene combustion[J]. International Journal of Hydrogen Energy, 2020, 45 (53): 29594- 29605 doi: 10.1016/j.ijhydene.2020.08.081

[13]	DING T, READSHAW T, RIGOPOULOS S, et al Machine learning tabulation of thermochemistry in turbulent combustion: an approach based on hybrid flamelet/random data and multiple multilayer perceptrons[J]. Combustion and Flame, 2021, 231: 111493 doi: 10.1016/j.combustflame.2021.111493

[14]	CHI C, JANIGA G, THÉVENIN D On-the-fly artificial neural network for chemical kinetics in direct numerical simulations of premixed combustion[J]. Combustion and Flame, 2021, 226: 467- 477 doi: 10.1016/j.combustflame.2020.12.038

[15]	FRANKE L L C, CHATZOPOULOS A K, RIGOPOULOS S Tabulation of combustion chemistry via artificial neural networks (ANNs): methodology and application to LES-PDF simulation of Sydney flame L[J]. Combustion and Flame, 2017, 185: 245- 260 doi: 10.1016/j.combustflame.2017.07.014

[16]	CHI C, XU X, THÉVENIN D Efficient premixed turbulent combustion simulations using flamelet manifold neural networks: a priori and a posteriori assessment[J]. Combustion and Flame, 2022, 245: 112325 doi: 10.1016/j.combustflame.2022.112325

[17]	IHME M, SCHMITT C, PITSCH H Optimal artificial neural networks and tabulation methods for chemistry representation in LES of a bluff-body swirl-stabilized flame[J]. Proceedings of the Combustion Institute, 2009, 32: 1527- 1535 doi: 10.1016/j.proci.2008.06.100

[18]	EMAMI M D, FARD A E Laminar flamelet modeling of a turbulent CH4/H2/N2 jet diffusion flame using artificial neural networks [J]. Applied Mathematical Modelling, 2012, 36 (5): 2082- 2093 doi: 10.1016/j.apm.2011.08.012

[19]	HANSINGER M, GE Y, PFITZNER M Deep residual networks for flamelet/progress variable tabulation with application to a piloted flame with inhomogeneous inlet[J]. Combustion Science and Technology, 2022, 194 (8): 1587- 1613 doi: 10.1080/00102202.2020.1822826

[20]	SHADRAM Z, NGUYEN T M, SIDERIS A, et al. Neural network closure models for estimating flame variables in a liquid-propellant rocket engine [C]// AIAA Scitech 2019 Forum. San Diego: [s.n.], 2019: 2008.

[21]	OWOYELE O, KUNDU P, AMEEN M M, et al Application of deep artificial neural networks to multi-dimensional flamelet libraries and spray flames[J]. International Journal of Engine Research, 2020, 21 (1): 151- 168 doi: 10.1177/1468087419837770

[22]	DEMIR S, KUNDU P, NUNNO A C, et al. Deep neural network based unsteady flamelet progress variable approach in a supersonic combustor [C]// AIAA SCITECH 2022 Forum. San Diego: [s.n.], 2022: 2073.

[23]	KASUYA H, IWAI Y, ITOH M, et al LES/flamelet/ANN of oxy-fuel combustion for a supercritical CO2 power cycle [J]. Applications in Energy and Combustion Science, 2022, 12: 100083 doi: 10.1016/j.jaecs.2022.100083

[24]	OWOYELE O, KUNDU P, PAL P Efficient bifurcation and tabulation of multi-dimensional combustion manifolds using deep mixture of experts: an a priori study[J]. Proceedings of the Combustion Institute, 2021, 38 (4): 5889- 5896 doi: 10.1016/j.proci.2020.09.006

[25]	JACOBS R A, JORDAN M I, BARTO A G Task decomposition through competition in a modular connectionist architecture: the what and where vision tasks[J]. Cognitive Science, 1991, 15 (2): 219- 250 doi: 10.1207/s15516709cog1502_2

[26]	MA J, ZHAO Z, YI X, et al. Modeling task relationships in multi-task learning with multi-gate mixture-of-experts: KDD'18 [C]// Proceeding of the 24th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. [S.l.]: ACM, 2018: 1930-1939.

[27]	ZHANG Y, WANG H, BOTH A, et al Effects of turbulence-chemistry interactions on auto-ignition and flame structure for n-dodecane spray combustion[J]. Combustion Theory and Modelling, 2019, 23 (5): 907- 934 doi: 10.1080/13647830.2019.1600722

[28]	HUANG Z, ZHAO M, XU Y, et al Eulerian-lagrangian modelling of detonative combustion in two-phase gas-droplet mixtures with OpenFOAM: validations and verifications[J]. Fuel, 2021, 286: 119402 doi: 10.1016/j.fuel.2020.119402

[29]	CROWE C T, SHARMA M P, STOCK D E The particle-source-in cell (PSI-CELL) model for gas-droplet flows[J]. Journal of Fluids Engineering, 1977, 99 (1): 325- 332

[30]	JENNY P, ROEKAERTS D, BEISHUIZEN N Modeling of turbulent dilute spray combustion[J]. Progress in Energy and Combustion Science, 2012, 38 (6): 846- 887 doi: 10.1016/j.pecs.2012.07.001

[31]	WANG Y, CAI R, SHAO C, et al A priori and a posteriori studies of a novel spray flamelet tabulation methodology considering evaporation effects[J]. Fuel, 2023, 331: 125892 doi: 10.1016/j.fuel.2022.125892

[32]	WANG Y C, SHAO C, LUO K, et al LES of a turbulent lifted methanol spray flame using a novel spray flamelet/progress variable model[J]. Energy, 2023, 284: 128608

[33]	WANG Y, SHAO C, JIN T, et al Large eddy simulation of spray combustion using the spray flamelet/progress variable model: further extension and validation[J]. Physics of Fluids, 2023, 35 (10): 105156

[34]	MAIONCHI D O, SANTOS F P, MELGUIZO-GAVILANES J, et al A generalised spray-flamelet formulation by means of a monotonic variable[J]. Combustion Theory and Modelling, 2021, 25 (2): 293- 314 doi: 10.1080/13647830.2020.1866215

[35]	WATANABE H, KUROSE R, HWANG S M, et al Characteristics of flamelets in spray flames formed in a laminar counterflow[J]. Combustion and Flame, 2007, 148 (4): 234- 248 doi: 10.1016/j.combustflame.2006.09.006

[36]	FRANZELLI B, VIÉ A, IHME M On the generalisation of the mixture fraction to a monotonic mixing-describing variable for the flamelet formulation of spray flames[J]. Combustion Theory and Modelling, 2015, 19 (6): 773- 806 doi: 10.1080/13647830.2015.1099740

[37]	O'LOUGHLIN W, MASRI A R The structure of the auto-ignition region of turbulent dilute methanol sprays issuing in a vitiated co-flow[J]. Flow Turbulence and Combustion, 2012, 89 (1): 13- 35 doi: 10.1007/s10494-012-9388-x

[38]	PRASAD V N, MASRI A R, NAVARRO-MARTINEZ S, et al Investigation of auto-ignition in turbulent methanol spray flames using large eddy simulation[J]. Combustion and Flame, 2013, 160 (12): 2941- 2954 doi: 10.1016/j.combustflame.2013.07.004

[39]	PICHLER C, NILSSON E J K Reduced kinetic mechanism for methanol combustion in spark-ignition engines[J]. Energy and Fuels, 2018, 32 (12): 12805- 12813 doi: 10.1021/acs.energyfuels.8b02136

[40]	BOX G E P, COX D R An analysis of transformations[J]. Journal of the Royal Statistical Society: Series B (Methodological), 1964, 26 (2): 211- 243 doi: 10.1111/j.2517-6161.1964.tb00553.x

[41]	GLOROT X, BENGIO Y. Understanding the difficulty of training deep feedforward neural networks [C]// Proceedings of the 13th International Conference on Artificial Intelligence and Statistics. Sardinia: [s.n.], 2010: 249–256.

[42]	KINGMA D P, BA J L. Adam: a method for stochastic optimization [EB/OL]. (2017-01-30)[2023-03-01].　https://arxiv.org/pdf/1412.6980.pdf.

[43]	BHATIA B, DE A, ROEKAERTS D, et al Numerical analysis of dilute methanol spray flames in vitiated coflow using extended flamelet generated manifold model[J]. Physics of Fluids, 2022, 34 (7): 075111 doi: 10.1063/5.0098705

[1]	Yi-cun WANG,Jiang-kuan XING,Kun LUO,Hai-ou WANG,Jian-ren FAN. Solving combustion chemical differential equations via physics-informed neural network[J]. Journal of ZheJiang University (Engineering Science), 2022, 56(10): 2084-2092.

[2]	Zheng-wei GAO,Tai JIN,Chang-cheng SONG,Kun LUO,Jian-ren FAN. Application of artificial neural networks to supercritical flamelet model[J]. Journal of ZheJiang University (Engineering Science), 2021, 55(10): 1968-1977.

Viewed

Full text

Abstract

Cited

Shared

Discussed