Skip to main content

Advertisement

SpringerLink
Log in

Identification of twin-shaft gas turbine based on hybrid decoupled state multiple model approach

  • Application of soft computing
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

Monitoring control of industrial systems is essential for the good productivity and safety of installations and operators, with better performance that must be guaranteed. This is often challenging due to the nonlinearities and dynamic complexities of these systems, adding operating constraints and instability. Hence, the multi-models constitute then an adapted tool for the modeling of the nonlinear systems to characterize their dynamic behaviors. Indeed, this work proposes the implementation of a hybrid identification approach of the operating variables of a gas turbine, thus making it possible to interconnect the various linear sub-models with decoupled states in order to generate the global output of their nonlinear model, from the exploitation in real time of the turbine's input/output data. However, the suggested decoupled-state multi-model approach offers an interesting alternative to the optimization procedure of the estimated turbine parameters. By using gradient and Gauss–Newton algorithms, improved by genetic algorithms combined with NSGA-II in hybrid form, in order to converge toward the best solutions with an optimal cost function, the obtained implementation results show that this approach allows the convergence of the estimated turbine variables and describes its behavior in real time, with the guaranteed efficiency of the proposed decoupled state multi-model method.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21

Similar content being viewed by others

Data availability

Data supporting this study are included within the article, more details or information will be made available on request.

Abbreviations

\(i\) :

Index for the \(i{th}\) linear local model

\(j\) :

Index for the \(j{th}\) output of the gas turbine

\(f_{i}\) :

The dynamic behavior of the \(i{th}\) local linear models

\(\hat{y}_{i} \left( k \right)\) :

The output of the \(i{th}\) local linear models

\(y\left( k \right)\) :

The measured output of the considered nonlinear system

\(\hat{y}\left( k \right)\) :

Estimated output of the multiple model

\(N\) :

The number of measurements

\(\theta\) :

The parameter vector to be found

\(A_{i} ,B,C_{i,j} \;and\;D_{i,j}\) :

The matrices of state space model for the \(i{th}\) linear local model

\(N_{{\text{var}}}\) :

The dimension of \(\theta\) and the chromosome in GA

\(h\) :

Iteration index of the search method

\(\Delta\) :

Adjustment factor

\(D\left( h \right)\) :

The research direction

\(I\) :

Identity matrix

\(\lambda\) :

Regularization parameter

\(\hat{y}_{j} \left( {k,\theta } \right)\) :

The \(j{th}\) output of the multi-model

\(y_{j} \left( k \right)\) :

The actual \(j{th}\) output of the gas turbine

\(L\) :

Number of local linear models

\(\xi (k)\) :

The decision variables vector

\(\mu_{i} \left( {\xi \left( k \right)} \right)\) :

The activation function

\(w_{i} \left( \xi \right)\) :

The weighting functions

\(x\) :

The space vector

\(u\) :

The control vector

\(c_{i}\) :

Center of the Gaussian function used in the weighting functions

\(\sigma\) :

The dispersion used for the Gaussian function

NGP:

Speeds of the high-pressure turbine

NPT:

Speeds of the low-pressure turbine

HP:

High-pressure turbine

LP:

Low-pressure turbine

\(J_{{}}\) :

The cost function

\(\varepsilon \left( k \right)\) :

The error obtained in instant k

\(G_{{}} \left( {\theta \left( h \right)} \right)\) :

The gradient

\(H_{{}} \left( \theta \right)\) :

The Hessian matrix

\(Xs_{i} \left( k \right)\) :

The augmented state space model

\(Ys_{i} \left( k \right)\) :

The augmented output of the state space model

NSGA-II:

Non-dominated Sorting Genetic Algorithm

References

  • Abdelhafid B, Hafaifa A, Guemana M (2016) Gas turbine modeling based on fuzzy clustering algorithm using experimental data. Appl Artif Intell 30(1):29–51

    Google Scholar 

  • Aissat S, Hafaifa A, Iratni A, Guemana M (2021) Identification of two-shaft gas turbine variables using a decoupled multi-model approach with genetic algorithm. Periodica Polytechnica Mech Eng 65(3):229–245

    Google Scholar 

  • Aissat S, Hafaifa A, Iratni A, Guemana M, Chen XiaoQi (2022a) Exploitation of multi-models identification with decoupled states in twin shaft gas turbine variables for its diagnosis based on parity space approach. Int J Dyn Control 10:25–48

    Google Scholar 

  • Aissat S, Hafaifa A, Iratni A, Hadroug N, Chen XiaoQi (2022b) Fuzzy decoupled-states multi-model identification of gas turbine operating variables through the use their operating data. ISA Trans. https://doi.org/10.1016/j.isatra.2022.07.005

    Article  Google Scholar 

  • Alaoui M, Iratni A, Alshammari OS, Hafaifa A, Colak I, Guemana M (2022a) Stability and analysis of vibrations bifurcation based on dynamic modeling of a solar titan 130 gas turbine. J Mech Eng 72(2):1–14

    Google Scholar 

  • Alaoui M, Alshammari OS, Iratni A, Hafaifa A, Jerbi H (2022b) Gas turbine speed monitoring using a generalized predictive adaptive control algorithm. Stud Inf Control 31(3):87–96

    Google Scholar 

  • Antonio CG, Ramírez AB (2010) Speeding up a multiobjective genetic algorithm with constraints through artificial neuronal networks. Comput Aided Chem Eng 28:391–396

    Google Scholar 

  • Arroyo J, Spiessens F, Helsen L (2020) Identification of multi-zone grey-box building models for use in model predictive control. J Build Perform Simul 13(4):472–486

    Google Scholar 

  • Atia SB, Messaoud A, Abdennour RB (2018) An online identification algorithm of unknown time-varying delay and internal multimodel control for discrete non-linear systems. Math Comput Modell Dyn Syst 24(1):26–43

    MathSciNet  MATH  Google Scholar 

  • Bagua H, Hafaifa A, Iratni A, Guemana M (2021) Model variables identification of a gas turbine using a subspace approach based on input/output data measurements. Control Theory Technol 19:183–196

    MATH  Google Scholar 

  • Chen W, Yan J, Chen M, Li X (2010) Diversity of Pareto front: a multiobjective genetic algorithm based on dominating information. J Control Theory Appl 8:222–228

    MathSciNet  Google Scholar 

  • Chen Y, Cai G, Zhang Z, Huang Y (2014) Multi-field coupling dynamic modeling and simulation of turbine test rig gas system. Simul Model Pract Theory 44:95–118

    Google Scholar 

  • Chen S, Huang Q, Fei Xu (2022) A two-grid decoupled algorithm for a multi-dimensional darcy-brinkman fracture model. J Sci Comput 90:88

    MathSciNet  MATH  Google Scholar 

  • Chica M, Cordón Ó, Damas S (2011) An advanced multiobjective genetic algorithm design for the time and space assembly line balancing problem. Comput Ind Eng 61(1):103–117

    Google Scholar 

  • Cho YM, Srinavasan S, Jae-Hyuk Oh, Kim HS (2007) Modelling and system identification of active magnetic bearing systems. Math Comput Modell Dyn Syst 13(2):125–142

    MATH  Google Scholar 

  • Colette R, Prakash N, Benjamen A (1999) A multi-model view of process modelling. Requirements Eng 4(4):169–187

    Google Scholar 

  • Çunkaş M (2010) Intelligent design of induction motors by multiobjective fuzzy genetic algorithm. J Intell Manuf 21:393–402

    Google Scholar 

  • Daneshfar F, Bevrani H (2012) Multiobjective design of load frequency control using genetic algorithms. Int J Electr Power Energy Syst 42(1):257–263

    Google Scholar 

  • Djeddi C, Hafaifa A, Iratni A, Hadroug N, Chen XiaoQi (2021) Robust diagnosis with high protection to gas turbine failures identification based on a fuzzy neuro inference monitoring approach. J Manuf Syst 59:190–213

    Google Scholar 

  • Djeddi AZ, Hafaifa A, Hadroug N, Iratni A (2022) Gas turbine availability improvement based on long short-term memory networks using deep learning of their failures data analysis. Process Safety Environ Protect 159:1–25

    Google Scholar 

  • Elaziz MA, Lin Li KPN, Jayasena SX (2020) Multiobjective big data optimization based on a hybrid salp swarm algorithm and differential evolution. Appl Math Modell 80:929–943

    MathSciNet  MATH  Google Scholar 

  • Gonzalez SR, Van Nieuwenhuyse I (2020) A survey on kriging-based infill algorithms for multiobjective simulation optimization. Comput Op Res 116:104869

    MathSciNet  MATH  Google Scholar 

  • Gregor G, Lightbody G (2008) Nonlinear system identification: From multiple-model networks to Gaussian processes. Eng Appl Artif Intell 21(7):1035–1055

    Google Scholar 

  • Gubarev VF, Romanenko VD, Miliavskyi YuL (2019) Methods for finding a regularized solution when identifying linear multivariable multiconnected discrete systems. Cybern Syst Anal 55:881–893

    MATH  Google Scholar 

  • Gupta V, Pawar S (2022) An effective structure of multi-modal deep convolutional neural network with adaptive group teaching optimization. Soft Comput 26:7211–7232

    Google Scholar 

  • Hadroug N, Hafaifa A, Abdellah K, Chaibet A (2017) Dynamic model linearization of two shafts gas turbine via their input / output data around the equilibrium points. Energy 120:488–497

    Google Scholar 

  • Hadroug N, Hafaifa A, Alili B, Iratni A, Chen XiaoQi (2022) Fuzzy diagnostic strategy implementation for gas turbine vibrations faults detection: towards a characterization of symptom–fault correlations. J Vib Eng Technol 10:225–251

    Google Scholar 

  • Holland JH (1992) Genetic algorithms. Sci Am 267(1):66–73

    Google Scholar 

  • Hou G, Gong L, Huang C, Zhang J (2020) Fuzzy modeling and fast model predictive control of gas turbine system. Energy 200:117465

    Google Scholar 

  • Huang X, Li QM (2023) The legitimacy of decoupled dynamic flow stress equations and their representation based on discrete experimental data. Int J Impact Eng 173:104453

    Google Scholar 

  • Jiang X, Na J (2020) Online surrogate multiobjective optimization algorithm for contaminated groundwater remediation designs. Appl Math Model 78:519–538

    MathSciNet  MATH  Google Scholar 

  • Jiang L, Cao J, Xiong L (2019) Generalized multiobjective robustness and relations to set-valued optimization. Appl Math Comput 361:599–608

    MathSciNet  MATH  Google Scholar 

  • Kudela J, Matousek R (2022) Recent advances and applications of surrogate models for finite element method computations: a review. Soft Comput 26:13709–13733

    Google Scholar 

  • Lee K-M, Park C-W (2022) A study on the application of a genetic algorithm for the fault recovery of substations. J Electr Eng Technol 17:1631–1637

    Google Scholar 

  • Leith DJ, Leithead WE (1999) Analytic framework for blended multiple model systems using linear local models. Int J Control 72(7/8):605–619

    MathSciNet  MATH  Google Scholar 

  • Li DH, Zhu ZJ (2022) Three-dimensional decoupled modeling on curing simulation of composite laminated plates with damage. Mater Today Commun 33:104255

    Google Scholar 

  • Liu Z, Chen H, Peng L, Ye X, Sichen Xu, Zhang T (2022a) Feedforward-decoupled closed-loop fuzzy proportion-integral-derivative control of air supply system of proton exchange membrane fuel cell. Energy 240:122490

    Google Scholar 

  • Liu Y, Osorio J, Ossareh HR (2022b) Decoupled reference governors: a constraint management technique for MIMO systems. Int J Control 95(11):3050–3069

    MathSciNet  MATH  Google Scholar 

  • Mohseni SS, Yazdanpanah MJ, Noei AR (2017) Model order reduction of nonlinear models based on decoupled multi-model via trajectory piecewise linearization. Int J Control, Autom Syst 15:2088–2098

    Google Scholar 

  • Muammer T, Hanbay D, Sengur A (2022) Multi-model LSTM-based convolutional neural networks for detection of apple diseases and pests. J Ambient Intell Humaniz Comput 13(7):3335–3345

    Google Scholar 

  • Nandola NN (2008) Sharad Bhartiya, A multiple model approach for predictive control of nonlinear hybrid systems. J Process Control 18(2):131–148

    Google Scholar 

  • Oliveira MA, Pellanda PC, Ades R, Silveira BP (2019) Time data based iterative method for frequency domain multivariable systems identification by optimized expansion of rational functions. J Control, Autom Electr Syst 30:666–676

    Google Scholar 

  • Ouyang L, Zhu S, Ye K, Park C, Wang M (2022) Robust Bayesian hierarchical modeling and inference using scale mixtures of normal distributions. IISE Trans 54(7):659–671

    Google Scholar 

  • Rahmoune MB, Hafaifa A, Kouzou A, Chen XiaoQi, Chaibet A (2021) Gas turbine monitoring using neural network dynamic nonlinear autoregressive with external exogenous input modelling. Math Comput Simul 179:23–47

    MathSciNet  MATH  Google Scholar 

  • Senhaji K, Ramchoun H, Ettaouil M (2020) Training feedforward neural network via multiobjective optimization model using non-smooth L1/2 regularization. Neurocomputing 410:1–11

    Google Scholar 

  • Stelios K (2006) Modelling fish growth: model selection, multi-model inference and model selection uncertainty. Fish Res 81(2/3):229–235

    Google Scholar 

  • Sun R, Liu Y, Zhu H, Azizipanah-Abarghooee R, Terzija V (2019) A network reconfiguration approach for power system restoration based on preference-based multiobjective optimization. Appl Soft Comput 83:105656

    Google Scholar 

  • Turkyilmaz A, Senvar O, Ünal İ, Bulkan S (2022) A hybrid genetic algorithm based on a two-level hypervolume contribution measure selection strategy for bi-objective flexible job shop problem. Comput Oper Res 141:105694

    MathSciNet  MATH  Google Scholar 

  • Yan J, Qin G, Sun M, Liang Y, Zhang Z (2022) Dimension decoupling attention mechanism for time series prediction. Neurocomputing 494:160–170

    Google Scholar 

  • Yang J, Li Y, Kim J (2022) Totally decoupled implicit–explicit linear scheme with corrected energy dissipation law for the phase-field fluid vesicle model. Comput Methods Appl Mech Eng 399:115330

    MathSciNet  MATH  Google Scholar 

  • Ye Q, Ouyang Z, Chen C, Yang X (2022) Efficient decoupled second-order numerical scheme for the flow-coupled Cahn-Hilliard phase-field model of two-phase flows. J Comput Appl Math 405:113875

    MathSciNet  MATH  Google Scholar 

  • Yusoff Y, Ngadiman MS, Zain AM (2011) Overview of NSGA-II for optimizing machining process parameters. Procedia Eng 15:3978–3983

    Google Scholar 

  • Zain AM, Haron H, Sharif S (2011) Optimization of process parameters in the abrasive waterjet machining using integrated SA–GA. Appl Soft Comput 11(8):5350–5359

    Google Scholar 

  • Zhang G (2022) Research on safety simulation model and algorithm of dynamic system based on artificial neural network. Soft Comput 26:7377–7386

    Google Scholar 

  • Zhang Yu, García MM, Kalawsky RS, Latimer A (2020) Grey-box modelling of the swirl characteristics in gas turbine combustion system. Measurement 151:107266

    Google Scholar 

  • Zhao G, Li H, Song Z (2016) Tensor product model transformation based decoupled terminal sliding mode control. Int J Syst Sci 47(8):1791–1803

    MathSciNet  MATH  Google Scholar 

Download references

Funding

All authors declare that no funding is provided for this work,

Author information

Authors and Affiliations

  1. Applied Automation and Industrial Diagnostics Laboratory, Faculty of Science and Technology, University of Djelfa, 17000, Djelfa, DZ, Algeria

    Sidali Aissat & Ahmed Hafaifa

  2. Faculty of Science and Technology, University Mohamed El Bachir El Ibrahimi of Bordj Bou Arreridj, 34030, El Anasser, DZ, Algeria

    Abdelhamid Iratni

  3. Department of Electrical and Electronics Engineering, Faculty of Engineering and Architecture, İstanbul Nisantasi University, 34398, Sarıyer, İstanbul, Turkey

    Ahmed Hafaifa & Ilhami Colak

  4. Faculty of Technology, University of Médéa, 26000, Médéa, DZ, Algeria

    Mouloud Guemana

  5. Department of Electrical Engineering, College of Engineering, University of Ha’il, Hail, 1234, Saudi Arabia

    Obaid S. Alshammari

Authors
  1. Sidali Aissat
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Abdelhamid Iratni
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ahmed Hafaifa
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Mouloud Guemana
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Obaid S. Alshammari
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Ilhami Colak
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Dr SA contributed to the concept and in the formulation of the hybrid identification problem for a dynamic nonlinear gas turbine, as well as contributed to the development of the method and performed the calculations and contributed to the drafting of the initial manuscript; Dr AI contributed to the formulation of the used multi-models for the identification of the studied gas turbine output variables, as well contributed to the correction of the language and writing of the final manuscript of this work, Prof. AH contributed to the formulation of optimization problem of the hybrid identification models applied to a gas turbine, by verifying the method and analyzing the obtained results, as well contributed to the drafting of the final manuscript with the interpretation the obtained results in this work; Prof. MG contributed to the processing of operating data of the examined turbine, as well contributed in the drafting by the final revision before the submission of this work; Dr. OSA contributed to the analysis and interpretation of the results after revision of the manuscript and to the synthesis of the used algorithms, as well as contributed to the drafting of the final revised revision; Prof. IC contributed to the drafting of the revised manuscript by the interpretation of the results after manuscript revision, as well contributed to the elaboration of the details of response to the technical comments of the reviewer's and carried out the analysis of the obtained results after revision,

Corresponding author

Correspondence to Ahmed Hafaifa.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

All authors declare that this work does not contain any studies with human participants or animals performed by any of the authors.

Informed consent

All authors agree for the publication of this work in Soft Computing Journal.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Aissat, S., Iratni, A., Hafaifa, A. et al. Identification of twin-shaft gas turbine based on hybrid decoupled state multiple model approach. Soft Comput 27, 17267–17289 (2023). https://doi.org/10.1007/s00500-023-08059-2

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-023-08059-2

Keywords

Search

Navigation