 Case report
 Open Access
Gas turbine modeling using adaptive fuzzy neural network approach based on measured data classification
 Abdelhafid Benyounes^{1},
 Ahmed Hafaifa^{1}Email author,
 Abdellah Kouzou^{1} and
 Mouloud Guemana^{2}
https://doi.org/10.1186/s4092901600063
© The Author(s) 2016
 Received: 14 February 2016
 Accepted: 26 May 2016
 Published: 22 July 2016
Abstract
The use of gas turbines is widespread in several industries such as; hydrocarbons, aerospace, power generation. However, despite to their many advantages, they are subject to multiple exploitation problem that need to be solved. Indeed, the purpose of the present paper is to develop mathematical models of this industrial system using an adaptive fuzzy neural network inference system. Where the knowledge variables in this complex system are determined from the real time input/output data measurements collected from the plant of the examined gas turbine. It is obvious that the advantage of the neurofuzzy modeling is to obtain robust model, which enable a decomposition of a complex system into a set of linear subsystems. On the other side, by focusing on the membership functions for residual generator to get consistent settings based on the used data structure classification and selection, where the main goal is to obtain a robust system information to ensure the supervision of the examined gas turbine.
Keywords
 Gas turbine
 Adaptive fuzzy neural network
 Fuzzy inference modeling
 Fuzzy clustering
 Data measurements
Background
Gas turbines have become very effective in industrial applications for electric and thermal energy production in several industries. However, these rotating machines systems are complex and they are composed of several sensitive elements that are subject to some defects and operational risks [1–6, 7]. In the literature, several scientific studies have been done as tentative to the model development for the analysis of the dynamic behavior of these types of gas turbine machinery. On the other side, the physical model of a gas turbine can be obtained by dynamic simulations in the conception step, or based on real plant data of these types of machine in exploitation. Indeed, the models developed in the literature screens are complicated and are not exploitable in control strategy [8–13].
The developed model in this paper is reliable and easy to be implemented to ensure the control of the gas turbine system, which can provide a quick and an accurate estimation of the dynamic behavior of the studied gas turbine using the identification techniques based on the fuzzy neural networks. This model can be a suitable choice for the detection and the isolation of faults in gas turbine based on the generation of residues resulting from the comparison of the actual process variables measurements and the referential model output. It also helps to understand the dynamics of the gas turbine, suitable for the control system design based on predictive model of the gas turbine, which provides an acceptable quality prediction.
This paper presents a nonlinear model structure using the fuzzy clustering method and the adaptive fuzzy neural network inference system [14–17]. This structure was tested by the use of the real operational data obtained from a SOLAR TITAN 130 gas turbine which is being used for the gas injection application. An evaluation of this model is presented by comparing it with nonlinear autoregressive exogenous NARAX modeling method. Furthermore, several robustness tests were conducted in this work to validate the proposed fuzzy model. Indeed, the measured data observed in the input/output of the examined SOLAR TITAN 130 allowed to achieve the realtime modeling. On the other side, this phase has helped to identify the adequate model which can be exploited in the control of the studied gas turbine by the determination of some rules needed for the supervision of such system.
Industrial application
The gas turbine studied in this work (Solar Titan 130) is installed at the gas compression station SC3 SONATRACH Djelfa, Algeria. This gas turbine is composed of three most important sections: Axial compressor, combustion chamber and the turbine. It is obvious that the inlet guide vane (IGV) variable is located in the inlet of the axial compressor and the nozzle guide vane (NGV) is located in the turbine section [1].
Examined gas turbine specifications
Quantity  Value 

Output Power  15 290 kW (20,500 hp) 
Heat Rate  9940 kJ/kWhr (7025 Btu/hphr) 
Exhaust Flow  180050 kg/hr (396,940 lb/hr) 
Exhaust Temperature  505 °C (940 °F) 
Max Speed  8855 rpm 
Gas turbine modeling
In this paper, the fuzzy clustering is used for the initial study using a Takagi Sugeno inference system to determine the set of fuzzy rules. These rules given the fuzzy models of the dynamic behavior based on real data of the examined gas turbine. The fuzzy cmeans clustering requires the existence of a multiple input and output data for the validations tests. This structure is used like an initial fuzzy inference system for the preparation of the adaptive fuzzy neural network inference system [18–20].
Algorithm of fuzzy clustering
Where Z is the data set, U = [μ _{ ik }] is the matrix of fuzzy partition (c × N), V = [v _{1}, v _{2}, … v _{ c }] is the vector of the center of classes to be determined, v _{ i } ∈ R ^{ n } is the center of the i ^{ th } class 1 < i < c, m ∈ [1, + ∞] is a factor that denotes the degree of fuzziness of the partition.

Step 1: Calculation of the cluster centers$$ {v}_i^l=\frac{{\displaystyle {\sum}_{K=1}^N{\left({\mu_{ik}}^{\left(l1\right)}\right)}^m{z}_k}}{{\displaystyle {\sum}_{K=1}^N{\left({\mu_{ik}}^{\left(l1\right)}\right)}^m}}\kern0.5em 1\le i\le c $$

Step 2: Calculation of the distances$$ {D}_{ikA}^2={\left({z}_k{v}_i^l\right)}^TA\left({z}_k{v}_i^l\right)\kern1.5em 1\le i\le c,1\le k\le N $$

Step 3: Updating the partition matrix
If D _{ ikA } ^{2} > 0 for 1 ≤ i ≤ c, 1 ≤ k ≤ N$$ {\mu}_{ik}^{(1)}=\frac{1}{{\displaystyle {\sum}_j^c1{\left(\frac{D_{ikA}}{D_{jkA}}\right)}^{\frac{2}{m1}}}} $$
Where the function 1(.) equal to 1 for the positive values of the partition matrix and −1 for the negative values pf this matrix. When m = 1 the partition matrix become zero (all terms are zero). Otherwise \( {\mu}_{ik}^{(1)}=0 \) if D _{ ikA } > 0 and \( {\mu}_{ik}^{(1)}\in \left[0,1\right] \) with \( {\displaystyle {\sum}_i^c{\mu}_{ik}^{(1)}}=1 \) too ‖U ^{(1)} − U ^{(l − 1)}‖ < ε.
Adaptive fuzzy neural network system
Where: m is the number of inputs, r is the number of rules, NMF is the number of membership functions for each rule, c _{ ij } is the mean value, σ _{ ij } is the variance of each membership function, f _{ k } is the consequent part function and P _{ kj } represents the scalar coefficients.
Where: y(t) is the output signal, u(t) is the input signal, n _{ a } is the number of output regression, n _{ b } is the number of intput regression and F is the nonlinear estimated function.
Where: n = n _{ a } + n _{ b } are scalar coefficients, x _{ i }(t) is the input data regression, k is the nonlinearity degree in the estimated function F.
Gas turbine investigation
Axial compressor
High pressure shaft (HP)
Low pressure shaft (LP)
Exhaust system (ET)
Where F _{ n }, n = 1, 2, …, 5 are fuzzy inference system variable that has been assembled from the real data of the examined turbine. TA and PA denote ambient temperature and pressure respectively, FF is fuel mass flow and T_{E} is exhausted temperature. Figure 4 shows the overall configuration of the system modeling. The parameter used for the comparison between the two models is the root mean square error (RMSE).
RMSE comparison between the two models
Gas turbine parameter  

Model type  HP shaft speed  LP shaft speed  ET system 
ANFIS model × 10^{3}  2,83  7,60  11,84 
NARX model × 10^{3}  7,10  21,30  23,21 
The implementation equations of the laws, governing the gas turbine system leads to knowledge model too complex and delicate implementation. In the case considered, the modeling techniques developed from input/output measures collected from the system examined yield to good results for exploitable modeling in control of the examined gas turbine system.
The obtained results of the dynamic behavior control in the examined gas turbines are satisfactory, such behavior is a very important issue in oil and gas industry; because for these uncontrolled dynamic action can lead to premature aging of the components of the turbine, or unacceptable noise and vibration. This is particularly important to develop a robust control system, in the context of having a good operation of gas turbines.
The proposed approach in this work, allows an effective and a reliable control system for the examined gas turbine. Initially, the contribution of the fuzzy techniques for the modeling of different control parameters of the examined gas turbine is studied. This allows to develop a global model based on fuzzy clustering method using algorithms based on fuzzy inference systems for classification of real data of the examined gas turbine. Secondly, the ability of the application of fuzzy models to the controller synthesis based on fuzzy logic system is studied. The obtained results in this work are satisfactory and show the effectiveness of the proposed approach.
Conclusion
This work has presented one of the major problems when looking for a reliable mathematical representation of gas turbine variables; the proposed ANFIS model provides a good improvement in performance during its operation. The use of the fuzzy clustering algorithm has an important advantage which allows the automatic generation of the membership functions of the fuzzy regions from the studied data. The obtained results from data classification with the associated models construction offer advantageous performance in modeling of the examined gas turbine system. This approach can provide reliable models for controlling of such systems.
Declarations
Competing interests
This paper presents a nonlinear model structure using the fuzzy clustering method and the adaptive fuzzy neural network inference system using the measurements input /output data from the examined gas turbine plant. The evaluation of this model is presented by comparing it with nonlinear autoregressive exogenous NARAX modeling method. Furthermore, several robustness tests were conducted in this work to validate the proposed fuzzy model. Indeed, the measured data observed in the input / output of the examined SOLAR TITAN 130 allowed to achieve the realtime modeling. Where the main goal is to obtain a robust system information to ensure the supervision of the examined gas turbine. The List of abbreviations is not present, all variables and parameters are given in the text of the manuscript.
Authors’ contributions
All authors read and approved the final manuscript.
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
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