天然气能量计量逆向混合建模数字孪生系统

刘彬; 钟璐; 冯全源; 陈毅红

doi:10.11999/JEIT260289

天然气能量计量逆向混合建模数字孪生系统

doi: 10.11999/JEIT260289 cstr: 32379.14.JEIT260289

刘彬^{1, 2},
钟璐²,
冯全源^1, ,,
陈毅红¹

1.
西南交通大学信息科学与技术学院成都 611700
2.
成都市秦川物联网科技股份有限公司成都 610100

基金项目: 国家自然科学基金重点项目(62531021)，四川省中央高校及科研院所科技成果转化项目(2025ZHCG0008)

详细信息

作者简介:
刘彬：硕士研究生(博士在读)，工程师，成都市产业建圈强链人才获得者，主要研究方向物联网、智慧能源与智能制造等

钟璐：硕士研究生，工程师，主要研究方向为物联网和智能制造等

冯全源：教授，四川省科技领军人才，主要研究方向集成电路设计、射频识别(RFID)、物联网等

陈毅红：教授，主要研究方向射频识别(RFID)、物联网以及人类活动识别等

通讯作者:
冯全源　fengquanyuan@swjtu.edu.cn

中图分类号: TP391.9; TN99
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- 被引次数: 0
出版历程
- 收稿日期: 2026-03-16
- 修回日期: 2026-04-22
- 录用日期: 2026-04-23
- 网络出版日期: 2026-05-23

An Inverse-Hybrid-Modeling Digital Twin System for Natural Gas Energy Metrology

LIU Bin^{1, 2},
ZHONG Lu²,
FENG Quanyuan^{1
, ,},
CHEN Yihong¹

1.
College of Information Science and Technology, Southwest Jiaotong University, Chengdu 611700, China
2.
Chengdu Qinchuan IoT Technology Co., Ltd., Chengdu 610100, China

Funds: The Project supported by the National Natural Science Foundation of China, (62531021), Sichuan Province Central Universities and Research Institutes Science and Technology Achievement Transformation Project, (2025ZHCG0008)

摘要

摘要: 针对传统天然气能量计量方法在复杂工况下存在动态响应延迟、参数辨识困难、物理简化过度及抗干扰能力弱等问题，该文提出一种基于逆向混合建模的天然气能量计量数字孪生系统。系统以“算法-系统-场景”3层级架构为核心，整合热值、流量、能量机理模型与多源实时数据流，引入变分自编码器(VAE)实现无监督工况特征挖掘，结合动态贝叶斯网络与变分期望最大化(VEM)系统校准构建参数自矫正循环，解决传统模型对海量标注数据的依赖。集成超声波流量计、气相色谱仪等工业级设备，保障数据实时传输与闭环控制。覆盖动态压力波动、含氢混合气、多气源切换等核心工况，确保模型与实际应用高度适配。通过全尺寸工业级实验平台25周连续验证，结果表明，系统运行延迟≤3.8 s，应用层端到端延迟抖动≤0.5 s，单设备日均能耗≤1.2 kW·h，平均无故障工作时间(MTBF)≥4 100 h，能量计量误差≤0.25%，热值误差≤0.12%，流量示值误差≤0.2%。同时，系统通过工业以太网加密与权限分级控制满足安全需求，为智能管网优化与标准化集成提供工程支撑。
- 天然气能量计量 /
- 数字孪生 /
- 逆向混合建模 /
- 变分自编码器 /
- 动态贝叶斯网络
Abstract: Objective Global natural gas consumption continues to increase at an average annual rate of 3.2%. A 0.1% reduction in energy measurement error can reduce trade disputes by approximately $750 million per year. Traditional studies mainly use indirect methods for energy measurement. Among these methods, chromatographic analysis and acoustic velocity correlation are the most widely used, but both have clear application limits. Chromatographic analysis has a low interference error, but it shows delayed dynamic response at high flow rates and limited dynamic calibration capability. It also has poor adaptability to multi-gas-source switching, requires manual calibration, and has high operation and maintenance costs. The lack of interoperability standards for energy networks further increases the difficulty of system integration. Acoustic velocity correlation provides a low-latency dynamic response for flow measurement, but it has a high interference error. This error may increase when the content of a single component changes, such as when the hydrogen content increases from 5% to 10%. The method may even fail under complex operating conditions, such as multi-gas-source mixing and dynamic pressure fluctuations. To address these issues, new mechanism-modeling-oriented methods have been developed. The two most representative directions are mechanism-modeling-driven methods and hybrid-modeling methods. Both methods combine multi-source data fusion with virtual-physical interaction to establish mechanism models that link flow rate, other parameters, and energy. These methods provide a new approach for accurate energy measurement, but new challenges remain. Mechanism-modeling-driven methods are usually based on static flow modeling using Computational Fluid Dynamics (CFD). However, their dynamic parameter updates are slow, with delays of more than 30 s. They also have difficulty adapting to real-time operating-condition changes, rely on large labeled datasets, and have limited interpretability. Hybrid-modeling methods still face unresolved problems in collaborative optimization across multiple modules. In addition, existing studies lack support from industrial-grade verification platforms. These limits restrict their ability to solve the dynamic response delay, parameter identification difficulty, excessive physical simplification, and weak interference resistance of traditional natural gas energy metrology methods under complex conditions. Based on recent progress in mechanism-modeling-driven and hybrid-modeling methods, this study proposes an inverse-hybrid-modeling-driven digital twin system. The system introduces a Variational AutoEncoder (VAE)-based operating-condition feature extraction algorithm and a Dynamic Bayesian Network (DBN)-based parameter calibration mechanism. It also uses a Variational Expectation-Maximization (VEM) algorithm for offline calibration. The proposed system aims to improve the accuracy, adaptability, and interference resistance of natural gas energy metrology under complex operating conditions. Methods A natural gas energy metrology digital twin system based on inverse hybrid modeling is proposed. The system is built on a three-tier “algorithm-system-scenario” architecture. It integrates calorific value, flow, and energy mechanism models with multi-source real-time data streams. The VAE is used for unsupervised mining of operating-condition features. A parameter self-correction loop is then constructed by combining the DBN with VEM-based system calibration. Industrial-grade devices, including ultrasonic flowmeters and gas chromatographs, are integrated to ensure real-time data transmission and closed-loop control. The system covers key operating conditions, including dynamic pressure fluctuations, hydrogen-blended gas mixtures, and multi-gas-source switching. This design ensures strong adaptability between the model and practical applications. The system was continuously verified for 25 weeks on a full-scale industrial-grade experimental platform. The results show an operational delay of ≤3.8 s, data transmission jitter of ≤0.5 s, average daily energy consumption per device of ≤1.2 kW·h, Mean Time Between Failures (MTBF) of ≥4 100 h, energy measurement error of ≤0.25%, calorific value error of ≤0.12%, and flow indication error of ≤0.2%. The system also meets security requirements through industrial Ethernet encryption and hierarchical access control. It provides engineering support for intelligent pipeline-network optimization and standardized integration. Results and Discussions First, a multi-level hybrid modeling framework is established. Modular hybrid modeling is achieved through the algorithm-system-scenario three-tier architecture. Numerical methods combined with data are more flexible than purely analytical models and can represent complex multiphysics systems with fewer lumped physical parameters. These parameters may change during energy measurement under mechanical, energy, and hydrodynamic effects. The VAE and DBN are used to deeply integrate mechanism models with real-time data. This reduces the parameter synchronization delay to 3.8 s and supports fluid-acoustic co-simulation and rapid response under complex operating conditions, such as hydrogen-blended natural gas. Second, an integrated algorithm for inverse hybrid modeling and system calibration is proposed. By incorporating the VAE, DBN, and VEM algorithm, the inverse hybrid modeling algorithm forms a self-supervised, adaptive intelligent system with an internal closed-loop operation. The VAE encoder compresses high-dimensional operating-condition data into low-dimensional feature vectors. This enables unsupervised feature extraction without large labeled datasets. Based on the learned internal data distribution, the VAE can also generate perturbed data similar to the input data. These data are used to simulate abnormal operating conditions and verify interference resistance. The DBN constructs a continuous “prior-evidence-posterior” iterative cycle to support system self-correction and adaptive response to operating-condition changes. The VEM algorithm compensates for systematic errors that are difficult for the DBN to capture, thereby overcoming the limits of traditional static models. Conclusions This study describes and validates a hybrid digital twin system that combines experimental data-driven methods with physical models. The system successfully simulates the physical characteristics of natural gas energy metrology. A full-scale test platform was constructed, and the main system parameters were validated using experimental measurement data and compared with industry benchmarks. Each independent module in the algorithm-system-scenario three-tier hybrid modeling architecture, including calorific value measurement, flow calculation, and energy conversion, was continuously verified for 25 weeks. The results confirm strong consistency between model predictions and actual measurements. On the natural gas energy metrology digital twin experimental platform, systematic validation was performed for three core functions: flow measurement under dynamic conditions, multi-component calorific value determination, and energy accumulation. The results show that the output of the digital twin model matches the physical device measurement data with an accuracy of more than 99.5%. Under complex operating conditions, such as pressure pulsations and hydrogen-blended gas mixtures, the system maintains the measurement error within 0.5%. This performance is better than that of traditional methods and meets the Class A accuracy requirements for natural gas measurement. By introducing a multi-tier hybrid modeling framework, this study addresses the parameter identification difficulty and excessive physical simplification of traditional natural gas energy metrology methods. The integration of the VAE, DBN, and VEM algorithm enables unsupervised feature extraction under complex operating conditions and adaptive calibration of model parameters. This reduces dependence on prior physical knowledge and large labeled datasets. The experimental results show that the proposed method maintains high precision and strong stability under complex scenarios, including pressure pulsations and hydrogen-blended gas mixtures, where traditional models have difficulty providing accurate descriptions.
- Natural gas energy metrology /
- Digital twin /
- Inverse hybrid modeling /
- Variational AutoEncoder (VAE) /
- Dynamic bayesian network

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图 1 天然气超声波流量计计量原理图

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图 2 时差式超声波流量计原理图

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图 3 VAE网络结构示意图

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图 4 数字孪生架构

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图 5 数字孪生实施流程图

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图 6 “算法-系统-场景”3层级混合建模架构图

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图 7 天然气能量计量实验平台原理

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图 8 能量计量实验平台

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图 9 天然气能量计量数字孪生平台

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图 10 压缩因子计算的不确定度范围

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图 11 天然气流量测量示值误差

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图 12 天然气周发热量

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图 13 天然气周发热量标准偏差

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表 1 基础参数与符号定义

符号	定义	单位
Z	天然气混合气体压缩因子(无量纲)	-
Z_j	组分j的压缩因子	-
b_j	组分j的求和因子(b_j=1–Z_j)	-
ρ_m	摩尔密度	kmol/m³
H_s	计量参比条件下高位发热量，30≤H_s≤45	MJ/m³
d	相对密度(空气=1, 20℃, 101.325 kPa)，0.55≤d≤0.80	-
$x_{{\rm{CO}}_2} $	气体混合物中不可燃的非烃组分含量，即CO₂的摩尔分数，0≤$x_{{\rm{CO}}_2} $≤0.20	-
$ x_{{\mathrm{H}}_2} $	气体混合物中可燃的非烃组分含量即H₂的摩尔分数，0≤$x_{{\mathrm{H}}_2} $≤0.10	-
p	绝对压力，0≤p≤12	MPa
T	热力学温度，263≤T≤338	K
B	第2维利系数，为H_s, d, $ x_{{\mathrm{CO}}_2} $, $x_{{\mathrm{H}}_2} $, T的函数	m³/kmol
C	第3维利系数，为H_s, d, $ x_{{\mathrm{CO}}_2} $, $x_{{\mathrm{H}}_2} $, T的函数	m⁶/kmol²
R	摩尔气体常数，R=0.008 314 510	MJ/(kmol·K)

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表 2 计量参比条件(20℃, 101.325 kPa)下天然气中常见组分的摩尔质量及物性参数

序号	组分	摩尔质量 M_j(kg/kmol)	理想体积发热量 $ \tilde{H}_{j}^{0} $(MJ/m³)	理想摩尔发热量 $ \overline{H}_{j}^{0} $(MJ/kmol)	理想质量发热量 $ \hat{H}_{j}^{0} $(MJ/kg)	压缩因子 Z_j	求和因子 $ \sqrt{{b}_{j}} $
1	甲烷 C₁	16.043	37.044	891.09	55.545	0.9981	0.0436
2	乙烷 C₂	30.070	64.91	1561.41	51.93	0.9920	0.0894
3	丙烷 C₃	44.097	92.29	2220.13	50.35	0.9834	0.1288
4	正丁烷 n-C₄	58.123	119.66	2878.57	49.53	0.9682	0.1783
5	异丁烷 i-C₄	58.123	119.28	2869.38	49.37	0.9710	0.1703
6	正戊烷 n-C₅	72.150	147.04	3537.17	49.03	0.9450	0.2345
7	异戊烷 i-C₅	72.150	146.76	3530.24	48.93	0.9530	0.2168
8	新戊烷 Neo-C₅	72.150	146.16	3516.01	48.73	0.9590	0.2025
9	己烷 C₆	86.177	174.46	4196.58	48.70	0.9190	0.2846
10	氮气 N₂	28.0135	0	0	0	0.9997	0.0173
11	氦气 He	4.0026	0	0	0	1.0005	0.0000
12	二氧化碳 CO₂	44.010	0	0	0	0.9650	0.1871
13	氢气 H₂	2.0159	11.889	285.99	141.87	1.0006	–0.0051
14	硫化氢 H₂S	34.082	23.37	562.19	16.50	0.9900	0.1000
15	水 H₂O	18.0153	1.84	44.224	2.45	0.9520	0.2191

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表 3 纯气体第二维利系数和非同类交互作用维利系数温度展开式中b(0), b(1), b(2)的数值

	ij	b(0)	b(1)	b(2)
CH	H0	–4.25468×10^–1	2.86500×10^–3	–4.62073×10^–6
CH	H1	8.77118×10^–4	–5.56281×10^–6	8.81510×10^–9
CH	H2	–8.24747×10^–7	4.31436×10^–9	–6.08319×10^–12
N₂	22	–1.44600×10^–1	7.40910×10^–4	–9.11950×10^–7
CO₂	33	–8.68340×10^–1	4.03760×10^–3	–5.16570×10^–6
H₂	44	–1.10596×10^–3	8.13385×10^–5	–9.87220×10^–8
CO	55	–1.30820×10^–1	6.02540×10^–4	–6.44300×10^–7
CH+N₂	12	y = 0.72 + 1.875 × 10^–5 (320 – T)²
CH+CO₂	13	y = –0.865
CH+H₂	14	–5.21280×10^–2	2.71570×10^–4	–2.50000×10^–7
CH+CO	15	–6.87290×10^–2	–2.39381×10^–6	5.18195×10^–7
N₂+CO₂	23	–3.39693×10^–1	1.161176×10^–3	–2.04429×10^–6
N₂+H₂	24	1.20000×10^–2	0	0

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表 4 基于验证集的不同扰动幅度下校准前后模型预测精度对比

VAE工况模式	扰动幅度	评估指标	校准前值	校准后值	提升率 (%)
稳态(C₀)	1%	NRMSE	0.0150	0.0080	46.67
		MAPE	0.0200	0.0120	40.00
		R²	0.9850	0.9920	0.71*
		鲁棒性	82%	98%	19.51
2 Hz流速波动(C₂)	2%	NRMSE	0.0300	0.0150	50.00
		MAPE	0.0350	0.0180	48.57
		R²	0.9750	0.9880	1.33*
		鲁棒性	75%	96%	28.00
含氢10%(C₄)	5%	NRMSE	0.0500	0.0200	60.00
		MAPE	0.0650	0.0300	53.85
		R²	0.9500	0.9800	3.16*
		鲁棒性	60%	92%	53.33
注：R²提升率计算方式为 $ \frac{\text{校准后}{R}^{2}\text{-校准前}{R}^{2}}{\text{1-校准前}{R}^{2}}×100\% $，更能反映对未解释方差的改善程度，结果分别为 46.67%, 52.00%, 60.00%。NRMSE和MAPE的提升率计算方式为 $ \frac{\text{校准前值-校准后值}}{\text{校准前值}}×100\% $。

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表 5 工业现场对比测试

指标	色谱分析法	声速关联法	本系统
热值误差(%)	±0.2	±1.8*	±0.12
流量示值误差(%)	±0.45	±0.8	±0.2
能量计量误差(%)	±0.5	±1.9	±0.25
流量动态响应速度(s)	60～120	40	3.8
多气源切换适应性	需人工校准	失效	自动切换
含氢工况适配性	需手动调整	含氢＞5%	VAE 自动识别+ 参数自适应
系统校准频次	2次/周	1次/周	1次/月
鲁棒性(%)	±0.5	±1.9	±0.25
资源消耗(kW·h)	1.8	1.9	1.2
数据传输稳定性	抖动≤2 s	抖动≤5 s	抖动≤0.5 s
安全性	基础加密	无独立加密机制，依赖现场网络隔离防护	工业以太网加密+ 权限分级(上位机)
*注：含氢＞5%时，声速关联法的热值误差急剧增大。流量动态响应速度定义为“从流量/组分变化发生 → 上位机能量数值首次稳定输出”的时间。本系统的热值误差为25周连续测试中95%置信区间的最大偏差。数据传输稳定性测试的是应用层端到端延迟抖动，包含了数据采集、预处理、模型计算等环节的排队延迟变化。

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