Dynamic simulation of gas turbines via feature similarity-based transfer learning

doi:10.1007/s11708-020-0709-9

Front. Energy

2020, Vol. 14

Issue (4) : 817-835 https://doi.org/10.1007/s11708-020-0709-9

RESEARCH ARTICLE

Dynamic simulation of gas turbines via feature similarity-based transfer learning

Dengji ZHOU, Jiarui HAO, Dawen HUANG, Xingyun JIA, Huisheng ZHANG(

)

Key Laboratory of Power Machinery and Engineering (Ministry of Education), Shanghai Jiao Tong University, Shanghai 200240, China

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Abstract

Since gas turbine plays a key role in electricity power generating, the requirements on the safety and reliability of this classical thermal system are becoming gradually strict. With a large amount of renewable energy being integrated into the power grid, the request of deep peak load regulation for satisfying the varying demand of users and maintaining the stability of the whole power grid leads to more unstable working conditions of gas turbines. The startup, shutdown, and load fluctuation are dominating the operating condition of gas turbines. Hence simulating and analyzing the dynamic behavior of the engines under such instable working conditions are important in improving their design, operation, and maintenance. However, conventional dynamic simulation methods based on the physic differential equations is unable to tackle the uncertainty and noise when faced with variant real-world operations. Although data-driven simulating methods, to some extent, can mitigate the problem, it is impossible to perform simulations with insufficient data. To tackle the issue, a novel transfer learning framework is proposed to transfer the knowledge from the physics equation domain to the real-world application domain to compensate for the lack of data. A strong dynamic operating data set with steep slope signals is created based on physics equations and then a feature similarity-based learning model with an encoder and a decoder is built and trained to achieve feature adaptive knowledge transferring. The simulation accuracy is significantly increased by 24.6% and the predicting error reduced by 63.6% compared with the baseline model. Moreover, compared with the other classical transfer learning modes, the method proposed has the best simulating performance on field testing data set. Furthermore, the effect study on the hyper parameters indicates that the method proposed is able to adaptively balance the weight of learning knowledge from the physical theory domain or from the real-world operation domain.

Keywords gas turbine dynamic simulation data-driven transfer learning feature similarity

Corresponding Author(s): Huisheng ZHANG

Online First Date: 09 December 2020 Issue Date: 21 December 2020

Cite this article:

Dengji ZHOU,Jiarui HAO,Dawen HUANG, et al. Dynamic simulation of gas turbines via feature similarity-based transfer learning[J]. Front. Energy, 2020, 14(4): 817-835.

URL:

https://academic.hep.com.cn/fie/EN/10.1007/s11708-020-0709-9
https://academic.hep.com.cn/fie/EN/Y2020/V14/I4/817

Components	System equations
Gas compressor	$T 2 = T 1 (η c + π c k c / (k c − 1) − 1) η c$
	$P 2 = P 1 π c$
	$η c = M A P c, η (T 1, P 1, π c, n c)$
	$Q c = M A P c, Q (T 1, P 1, π c, n c)$
High pressure turbine	$T 34 = T 3 1 − (1 − π h t k h t / (k h t − 1)) η h t$
	$P 34 = P 3 / π h t$
	$η h t = M A P h t, η (T 3, P 3, π h t, η h t)$
	$Q h t = M A P h t, Q (T 3, P 3, π h t, η h t)$
Low pressure turbine	$T 4 = T 34 1 − (1 − π p t k p t / (k p t − 1)) η p t$
	$P 4 = P 34 / π p t$
	$η p t = M A P p t, η (T 34, P 34, π p t, η p t)$
	$Q p t = M A P p t, Q (T 34, P 34, π p t, η p t)$

Tab.1 Characteristic map equations of components

Fig.1 Structure of RNN.

Fig.2 LSTM neuron structure.

Tab.2 Transfer learning methods

Fig.3 Gas turbine dynamic simulation system.

Tab.3 Set points of N_GG for 12 inputs

Fig.4 Examples of transient process simulation inputs.

Fig.5 Examples of 3 kinds of data sets.

Fig.6 Encoder-decoder neural networks.

Fig.7 Feature similarity-based transfer learning framework.

Fig.8 Field data sequence plotting.

Fig.9 Data preprocessing with sliding windows.

Tab.4 Prediction performance of 6 methods on testing data

Fig.10 Iteration of (a) MSE and (b) R² of 6 methods.

Fig.11 Reconstructed field and ideal transient simulation input via encoder-decoder networks.

Fig.12 R² of 6 methods on predictive output.

Fig.13 Comparison of 6 transfer learning methods on testing data 1.

Fig.14 Comparison of 6 methods on testing data 2.

Fig.15 Effect of simulation data sample size on R².

Fig.16 Effect of weighting factor β on R².

No.	Similarity metrics	Formulations
0	–	–
1	Pearson correlation	$d c o r r (V 1, V 2) = ∑ i = 1 m (V 1 i − V ¯ 1) ? (V 2 i − V ¯ 2) ∑ i = 1 m (V 1 i − V ¯ 1) 2 ? ∑ i = 1 m (V 2 i − V ¯ 2) 2$
2	Manhattan distance	$d m (V 1, V 2) = ∑ i = 1 m (V 1 i − V 2 i)$
3	Euclidean distance	$d e (V 1, V 2) = ∑ i = 1 m (V 1 i − V 2 i) 2$
4	Cosine distance (ours)	$d cos ? (V 1, V 2) = ∑ i = 1 m V 1 i ? V 2 i ∑ i = 1 m (V 1 i) 2 ? ∑ i = 1 m (V 2 i) 2$

Tab.5 Formulations of similarity metrics

Fig.17 Effect of metrics of feature similarity measurement on R².

R_g	Gas constant
T	Gas temperature/K
V	Volume/m³
HV	Fuel heating value/(kJ·kg^–1)
h	Enthalpy/(kJ·mol^–1)
c_p,g	Heat capacity/(J·K^–1)
$ρ$	Combustor gas density/(kg·m^–3)
NET_sim	Neural networks trained by simulation data set
NET_real	Neural networks trained by real-world data set
d	Distance metrics
MSE	Mean square error
Error	Relative error
I	Inertia moment/(kg·m^–2)
P	Pressure/Pa
N	Rotation speed/(r·min^–1)
D	Data set
X	Input signal tensor of simulation model
Y	Output signal tensor of simulation model
V	Encoded vector
L	Latent vector
W	Parameters of neural networks
β	Weighting factor
R²	R² score for regression
t	Turbine
c	Compressor
g	Gas
in	Inlet
out	Outlet
GG	Gas generator
PT	Power turbine
1	Inlet of the gas generator
2	Inlet of the combustor
3	Inlet of the high pressure turbine
34	Outlet of the gas generator
4	Outlet of the power turbine
field	Field data
sim1	Field signal-simulation data
sim2	Transient process simulation data

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