LMI feasibility analysis of 2DOF NATA model

Andrea Wéber; Miklós Kuczmann

doi:10.1556/606.2024.00888

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Pollack Periodica

Volume/Issue:: Volume 19: Issue 2

LMI feasibility analysis of 2DOF NATA model

Authors:

Andrea Wéber

Andrea Wéber Doctoral School of Multidisciplinary Engineering Sciences, Széchenyi István University, Győr, Hungary

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weber.andrea@sze.hu https://orcid.org/0009-0000-8283-5498

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Miklós Kuczmann

Miklós Kuczmann Department of Power Electronics and Electric Drives, Faculty of Power Electronics and Electric Drives, Széchenyi István University, Győr, Hungary

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Pages:: 22–29

Online Publication Date:: 19 Feb 2024

Publication Date:: 24 Jun 2024

Article Category:: Research Article

DOI:: https://doi.org/10.1556/606.2024.00888

Keywords:: tensor product transformation; linear matrix inequality; controller performance; reducing non-linearity; feasibility analysis

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Abstract

Present paper shows the different types of tensor product model based linear matrix inequality controller design and feasibility analysis of two degrees of freedom aeroelastic wing section model. The tensor product models are based on reducing or removing the nonlinear behavior of the system and weighting functions. The linear matrix inequality based method results globally asymptotically stable system. The goal of the paper is to examine that selecting and varying the transformation space influences the feasibility of the linear matrix inequality based controller. The paper gives a comparison between the different tensor product models in terms of controller performance. The linear matrix inequality gives feasible solution for the controller design if the transformation space is selected adequately.

Abstract

1 Notations and definitions

Notations and definitions that used in present paper are

Indices: $i = 1, 2, \dots, I$ and $j = 1, 2, \dots, J$ , where $I, J$ are the number of the Linear Time-Invariant system (LTI) vertexes;
System matrix $S (p (t))$ is determined with $p = p (t) \in Ω$ ;
Transformation space $Ω = [a_{1}, b_{1}] \times [a_{2}, b_{2}] \times . . . \times [a_{n}, b_{n}] \subset R^{n}$ , where the Tensor Product (TP) model representation is explainable;
Weighting functions $w_{i} = w_{i} (p (t))$ , $w_{j} = w_{j} (p (t))$ ;
Close to NOrmalised (CNO) type weighting function;
$x (t) \in R^{n}$ is the state vector, $u (t) \in R^{m}$ is the input vector, $y (t) \in R^{q}$ is the output vector and $A_{i} (t) \in R^{n \times n}$ , $B_{i} (t) \in R^{n \times m}$ ;
Matrices for Linear Matrix Inequality (LMI), $F_{i_{1}, i_{2}}$ is the controller gain, and $F_{i} = M_{i} P_{1}^{- 1}$ , $F_{j} = M_{j} P_{1}^{- 1}$ , where $P_{1} > 0$ . Matrices $P$ and $M$ can be found by convex optimization methods including LMIs;
X-type weighting functions: Varying the input space with reduction of non-linearity results less complex weighting functions, (see in Fig. 1) where $w_{n} (p_{n} (t))$ are illustrated for $n$ dimensions.

Fig. 1.

X-type weighting functions

Citation: Pollack Periodica 19, 2; 10.1556/606.2024.00888

2 Introduction

Present article shows the different types of TP models of the aeroelastic wing section with LMI based controller design in Parallel Distributed Compensation (PDC) framework via Higher Order Singular Value Decomposition (HOSVD). The proposed design method results stable controller and the paper proves that it can be selected the better TP model with better control performance. In order to achieve this, it is possible to vary the transformation space and select the parameter space.

Previous paper [1] describes the TP model transformation-based observer and controller design for the same Nonlinear Aeroelastic Test Apparatus (NATA) model. This paper presents that selecting the input space and transformation space has influence on the control performances. In the current paper, the parameters of the wing model, the state-space variables, and the quasi-Linear Parameter Varying (qLPV) state-space representation, the applied parameters and mathematical expressions are the same as in papers [1–3]. The TP transformation is executed on the “original” qLPV model, see in papers [2, 3]. Current paper presents several alternative TP models and shows the LMI feasibility analysis for these models.

Paper [4] proposes the nonlinearity reducing method and changing the number of the inputs for the TP model. The article describes a new type of method to the TP model transformation: how to vary the number of inputs of a given TP model. The paper focuses on how to manipulate the number of inputs of a given Takagi-Sugeno (TS) fuzzy model but also discusses the difference between TS fuzzy and TP models.

The TP model transformation and its extension, LMI and HOSVD based methods are a popular research field today, there are many publications about the investigation; [4–13]. Articles on practical applications of the TP model transformation: [14–24]. Additional papers used for current article: [25, 26].

Current paper presents that varying input space and transformation space has influence on the feasibility regions of LMI. In this paper, the weighting functions are all CNO types, the same grid density is applied for each TP models. Furthermore, if the nonlinearity is reduced, then the feasibility regions of LMI are increased. With these investigations, it can be determined which TP model results better control performance.

3 Novel contribution of the paper

Present paper investigates that reducing non-linearity from the TP models and selecting transformation space influence the design of LMI based controller and the TP model, respectively.

Statement 1. Reducing or removing the nonlinear behavior from the TP models results different TP models and different control performance and the feasibility regions are increased. Selecting the parameter space has influence on the feasibility regions of LMI.
Statement 2. Varying and selecting the transformation space influence the feasibility of the LMI based controller and the TP model. Selection of transformation space shows how the controller changes in LMIs, then it can be chosen the better controller performance. The feasibility test shows that the more the non-linearity decreases, the larger the feasibility region becomes.

Proves. The proves are based on the 2DoF aeroelastic wing section model. The examinations follow these key points:

Removing non-linearity from TP models: varying the input space;
Applying HOSVD based method in numerical way;
HOSVD and TP model transformation generates the LTI vertex systems;
LMI feasibility analysis: changing the transformation space;
LMI based controller design.

Versions of TP models have different numbers of inputs or combinations of inputs. The key structure for transforming TP models is based on the complexity reduction technique developed in [27], which presents a singular value-based method for reducing a given set of fuzzy rules. The method is able to change the number of inputs and transform the nonlinearity between the fuzzy rules and the input dimensions. These features significantly increase the modeling capability of the TP structure, allowing further complexity reduction and more robust control optimization.

In the present research, the reduction of nonlinearity is achieved by removing nonlinearities: reducing the order of the system and eliminating as much nonlinearity as possible from the system of equations, e.g., $\sin (x_{3})$ , $\cos (x_{3})$ , etc. Alternative TP models can be generated from the original TP model, with the advantage that alternative models can have a different number of inputs, or the inputs of the TP model can be specified as a function of the original inputs.

4 TP model variants of the wing section

The mechanical model (Fig. 2) is a two-dimensional typical airfoil in horizontal flow, whose motion is determined by two independent degrees of freedom; vertical displacement (dive) and pitch. The study of the dynamic behaviour of the aeroelastic wing is based primarily on divergence and rudder reversal. The mathematical modeling of the 2DoF aeroelastic wing section model and the parameters are presented in papers [2] and [3].

Fig. 2.

Two-dimensional airfoil plate

Citation: Pollack Periodica 19, 2; 10.1556/606.2024.00888

The state variables of the mechanical model are:

x (t) = [\begin{array}{c} x_{1} (t) \\ \begin{array}{c} x_{2} (t) \\ \begin{array}{c} x_{3} (t) \\ x_{4} (t) \end{array} \end{array} \end{array}] = [\begin{array}{c} h (t) \\ \begin{array}{c} α (t) \\ \begin{array}{c} \dot{h} (t) \\ \dot{α} (t) \end{array} \end{array} \end{array}],

(1)

where

x_{1} (t)

is the plunge displacement and

x_{2} (t)

is the pitch displacement. The qLPV state space representation of the model:

\dot{x} (t) = S (p (t)) [\begin{array}{c} x (t) \\ u (t) \end{array}],

(2)

where

p (t) = [\begin{array}{c} U (t) \\ x_{2} (t) \end{array}],

(3)

where

U (t)

is the free stream velocity and the system matrix is as follow:

S (p (t)) = [\begin{array}{l} S_{1} (p (t)) & S_{2} (p (t)) \end{array}],

(4)

S_{1} (p (t)) = [\begin{array}{l} 0 & 0 \\ 0 & 0 \\ - k_{1} & - k_{2} U^{2} (t) - p (k_{α} (x_{2} (t))) \\ - k_{3} & - k_{4} U^{2} (t) - q (k_{α} (x_{2} (t))) \end{array}],

(5)

S_{2} (p (t)) = [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ - c_{1} (U (t)) & - c_{2} (U (t)) & g_{3} U^{2} (t) \\ - c_{3} (U (t)) & - c_{4} (U (t)) & g_{4} U^{2} (t) \end{array}],

(6)

where the mathematical expressions and parameters are described in papers [2] and [3].

4.1 TP model 1

This model is the “original” TP model, where the parameters are not changed [2–4]. The weighting functions are CNO types for all TP models. After using HOSVD method on the system matrix (4), the following TP model transformation describes the nonlinear model:

\dot{x} ≅ \sum_{i = 1}^{3} ‍ \sum_{j = 1}^{2} ‍ w_{i} (U) w_{j} (x_{2}) (A_{i, j} x + B_{i, j} u),

(7)

where

u = - (\sum_{i = 1}^{3} ‍ \sum_{j = 1}^{2} ‍ w_{i} (x_{1}) w_{j} (x_{2}) F_{i, j}) x .

(8)

Therefore the number of LTI vertex models are $3 \times 2 = 6$ . Here, the parameters are $p_{1} (t) = U (t)$ , $p_{2} (t) = x_{2} (t)$ and the transformation space $Ω = [14, 25] \times [- 0.3, 0.3]$ with grid density $137$ . The weighting functions of TP model 1 are shown in Fig. 3. It can be seen that there are $w_{1, 1}, w_{1, 2}, w_{1, 3}$ weighting functions for $p_{1}$ , and $w_{2, 1}, w_{2, 2}$ weighting functions for $p_{2}$ . The next step is to remove or reduce the nonlinear behavior of the TP model 1.

Fig. 3.

Weighting functions of TP model 1

Citation: Pollack Periodica 19, 2; 10.1556/606.2024.00888

4.2 TP model 2

To reduce the nonlinearity, new parameter space is introduced:

p_{1} (t) = U (t)

and

p_{2} (t) = k_{α} (x_{2} (t))

. The transformation space is the same, as in case of the TP model 1. Here, the generated LTI vertex systems are

3 \times 2 = 6

\dot{x} ≅ \sum_{i = 1}^{3} ‍ \sum_{j = 1}^{2} ‍ w_{i} (U) w_{j} (k_{α} (x_{2})) (A_{i, j} x + B_{i, j} u) .

(9)

Figure 4 shows that $w_{1, 1}$ , $w_{1, 2}$ , $w_{1, 3}$ weighting functions of parameter $p_{1} (t)$ are the same as in case of TP model 1. $x_{2} (t)$ has influence on the system matrix. $w_{2, 1}$ , $w_{2, 2}$ are X-type weighting functions for $p_{2} (t)$ .

Fig. 4.

Weighting functions of TP model 2

Citation: Pollack Periodica 19, 2; 10.1556/606.2024.00888

The nonlinear behavior of the weighting functions are removed in the second dimension, therefore the dimension of $x_{2} (t)$ has changed. It can be noticed that the complexity of the second dimension is decreased compared to the first TP model.

4.3 TP model 3

Here, a new parameter is introduced:

p_{2} (t) = U^{2} (t)

, so the parameter space now is

p_{1} (t) = U (t)

p_{2} (t) = U^{2} (t)

p_{3} (t) = x_{2} (t)

and the transformation space

Ω = [14, 25] \times [1 4^{2}, 2 5^{2}] \times [- 0.3, 0.3]

. After executing HOSVD, there are

2 \times 2 \times 2 = 8

LTI vertex systems. The structure of the TP model transformation is as follow:

\dot{x} ≅ \sum_{i = 1}^{2} ‍ \sum_{j = 1}^{2} ‍ \sum_{k = 1}^{2} ‍ w_{i} (U) w_{j} (U^{2}) w_{k} (x_{2}) (A_{i, j, k} x + B_{i, j, k} u) .

(10)

The weighting functions $w_{1, 1}$ , $w_{1, 2}$ and $w_{2, 1}$ , $w_{2, 2}$ are X-type for parameters $p_{1} (t)$ and $p_{2} (t)$ . For $p_{3} (t)$ , $w_{3, 1}$ , $w_{3, 2}$ functions are illustrated in Fig. 5. In the first two dimensions, the weighting functions are less complex and there is a new dimension but the maximum number of the weighting functions are two. The number of the LTI systems are increased but reducing the nonlinear behavior is still possible.

Fig. 5.

Weighting functions of TP model 3

Citation: Pollack Periodica 19, 2; 10.1556/606.2024.00888

4.4 TP model 4

This TP model is the combination of TP model 2 and 3. The parameters are

p_{1} (t) = U (t)

p_{2} (t) = U^{2} (t)

and

p_{3} (t) = k_{α} (x_{2} (t))

, the transformation space is

Ω = [14, 25] \times [1 4^{2}, 2 5^{2}] \times [- 0.3, 0.3]

. Here, the number of the LTI system are

2 \times 2 \times 2 = 8

\dot{x} ≅ \sum_{i = 1}^{2} ‍ \sum_{j = 1}^{2} ‍ \sum_{k = 1}^{2} ‍ w_{i} (U) w_{j} (U^{2}) w_{k} (k_{α} (x_{2})) (A_{i, j, k} x + B_{i, j, k} u) .

(11)

The weighting functions $w_{1, 1}$ , $w_{1, 2}$ , $w_{2, 1}$ , $w_{2, 2}$ and $w_{3, 1}$ , $w_{3, 2}$ are all X-types. Therefore, it can be seen that the maximum number of the functions are two and this model is more simpler than the previous three TP models.

5 LMI feasibility analysis

Changing the transformation space $Ω$ has influence on the LMI feasibility regions. Therefore the analysis of the feasibility test shows whether or not exist solution for LMIs. Consider the following solver for LMI feasibleness problems $L (x) < R (x)$ , where $R$ is the feasibility radius. The solver is minimizes $t$ subject to $L (x) < R (x) + t I$ . Therefore, $t$ should be negative for feasible solution.

The analysis only includes the change of the transformation space in one dimension, i.e., the transformation space is not changed in several dimensions at the same time.

In the figures, x-axis shows $p_{\min}$ , y-axis shows $p_{\max}$ parameters. In the illustrations, it is presented that the LMI can be solved in the given interval in different dimensions. Thus, the regions marked with black dots are the feasible regions and the regions marked with empty circles are the non-feasible regions.

5.1 LMI feasibility regions of TP model 1

Figure 6 illustrates the LMI feasibility regions of the TP model 1. In the first case the transformation space is changed in the first dimension for parameter $p_{1} (t)$ and fixed in the second dimension on interval $[-, -] \times [- 0.3, 0.3]$ . The figures presents the regions of the LMI feasibility from $U = [1, 5]$ to $U = [40, 534]$ . The second case shows extending of the transformation space $Ω = [14, 25] \times [-, -]$ for parameter $p_{2} (t)$ .

Fig. 6.

LMI feasibility regions of TP model 1, a) first case, b) second case

Citation: Pollack Periodica 19, 2; 10.1556/606.2024.00888

5.2 LMI feasibility regions of TP model 2

The LMI feasibility regions of TP model 2 are the same as the previous model (Fig. 6) on the examined interval. It can be seen that the transformation space is changed in the first dimension related to $p_{1} (t)$ on interval $[-, -] \times [- 0.3, 0.3]$ . In the second case, the second dimension is changed on interval $[14, 25] \times [-, -]$ for parameter $p_{2} (t)$ . The figures show that the feasibility regions are the same within the interval considered, but the nonlinearity was removed. Feasibility growth occurs outside the examined interval.

5.3 LMI feasibility regions of TP model 3

Here, changing the transformation space is illustrated in Fig. 7. It can be seen that the first dimension is modified for $p_{1} (t) = U (t)$ and the others are fixed on interval $[-, -] \times [1 4^{2}, 2 5^{2}] \times [- 0.3, 0.3]$ . Then, the third dimension is changed and the first and second dimensions are fixed on interval $[14, 25] \times [1 4^{2}, 2 5^{2}] \times [-, -]$ for $p_{3} (t)$ . It can be noticed that the LMI feasibility region is increased for parameter $p_{1} (t)$ compared to previous TP models.

Fig. 7.

LMI feasibility regions of TP model 3, a) first case, b) second case

Citation: Pollack Periodica 19, 2; 10.1556/606.2024.00888

5.4 LMI feasibility regions of TP model 4

The LMI feasibility analysis shows that the LMI based controller is feasible and regions and given intervals are the same as TP model 3, see in Fig. 7, but feasibility regions can occur outside the examined interval. The first case illustrates when the transformation space is changed in the first interval and the second and third intervals are fixed on $[-, -] \times [1 4^{2}, 2 5^{2}] \times [- 0.3, 0.3]$ . The second case shows that the third dimension is changed in transformation space $[14, 25] \times [1 4^{2}, 2 5^{2}] \times [-, -]$ for parameter $p_{3} (t)$ . Consequently, this TP model covers larger LMI feasibility regions.

In summary, as the nonlinear property is gradually reduced, the LMI feasibility region increases, which can be proved by varying and extending the transformation space $Ω$ .

6 Stable controller design

The method of LMI allows the stability of the system to be achieved if LMI is feasible for different TP models. The polytopic model with controller is asymptotically stable if there exist such positive definite matrices

X > 0

and

M_{i}

satisfies the following conditions:

- X A_{i}^{T} - A_{i} X + M_{i}^{T} B_{i}^{T} + B_{i} M_{i} ≻ 0,

(12)

for all

i

\begin{array}{c} - X A_{i}^{T} - A_{i} X - X A_{j}^{T} - A_{j} X + M_{j}^{T} B_{i}^{T} + B_{i} M_{j} \\ + M_{i}^{T} B_{j}^{T} + B_{j} M_{i} ⪰ 0, \end{array}

(13)

for all $i < j \leq I$ and $\forall p (t) : w_{i} (p (t)) t)) p w_{j} (p (t)) = 0$ , where $i = 1, \dots, I$ , $j = i + 1, \dots, I$ and $I$ is the number of the LTI systems, from the feedback gain solutions $X$ and $M_{i}$ : $F_{i} = M_{i} X^{- 1}$ .

The initial conditions for all TP models are ${[h, α, \dot{h}, \dot{α}]}^{T} {= [0.01, 0.1, 0, 0]}^{T}$ . Figure 8 shows the $x_{1}$ and $x_{2}$ state variables i.e., plunge displacement $h$ and pitch displacment $α$ , the $u$ control signal of the wing section model. These figures also show the different TP models with reduced non-linearity. Therefore, TP models give different results for the LMI based controller in terms of stability. The present TP models are investigated based on the objective to reduce the oscillation rate for each model and to reach the steady state sooner.

Fig. 8.

State variables and control signals for all TP models, a) state variable x₁; b) state variable x₂; c) control signal u

Citation: Pollack Periodica 19, 2; 10.1556/606.2024.00888

It can be seen in case of state variables $x_{1}$ , the steady state is reached in about $0.4$ to $0.8$ seconds. The oscillation rate is highest between $0$ and $0.3$ seconds. The purple colour indicates the state variable $x_{1}$ of TP model 1, i.e. the “original system”. It can be noticed that the oscillations are larger for TP models 1 and 3. The figure shows that TP model 4 stabilizes faster and has smaller oscillation magnitude.

Furthermore, Fig. 8 shows that in case of state variables $x_{2}$ , the system stabilizes faster between about $0$ and $0.1$ seconds forTP models 1 and 3, but for TP models 2, 4, the function decays faster and the system reaches steady state faster because there is less oscillation. For the latter two models, stabilisation occurs between about $0.4$ and $0.8$ seconds. It is clear that TP model 3 performs better for state variable $x_{2}$ .

Finally, the control signal $u$ showed in Fig. 8, that illustrates that TP model 2 has better control performance. In case of TP model 1 and 3, the control signals have lower controller performance because the system takes longer to reach steady state.

7 Conclusion

Current paper presents the TP transformation based controller design of 2DoF aeroelastic wing section through HOSVD method in PDC framework. The controller is designed for each TP models and the controllers are accomplished with LMI based method. The paper gives a comparison between the TP models with different non-linearity via choosing parameter space and varying transformation spaces. Consequently, it can be noted that selecting transformation space and input space results different control performance. The LMI feasibility test shows that the smaller the nonlinearity, the larger the feasibility region of the TP models. Then, we can choose the better TP model with better control performance. As a result, the TP model 4 is the simpler model from point of reducing non-linearity and the controller performance.

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Pollack Periodica

Print ISSN:: 1788-1994

Online ISSN:: 1788-3911

Editorial Board

Bálint Bachmann (Institute of Architecture, Faculty of Engineering and Information Technology, University of Pécs, Hungary)
Jeno Balogh (Department of Civil Engineering Technology, Metropolitan State University of Denver, Denver, Colorado, USA)
Radu Bancila (Department of Geotechnical Engineering and Terrestrial Communications Ways, Faculty of Civil Engineering and Architecture, “Politehnica” University Timisoara, Romania)
Charalambos C. Baniotopolous (Department of Civil Engineering, Chair of Sustainable Energy Systems, Director of Resilience Centre, School of Engineering, University of Birmingham, U.K.)
Oszkar Biro (Graz University of Technology, Institute of Fundamentals and Theory in Electrical Engineering, Austria)
Ágnes Borsos (Institute of Architecture, Department of Interior, Applied and Creative Design, Faculty of Engineering and Information Technology, University of Pécs, Hungary)
Matteo Bruggi (Dipartimento di Ingegneria Civile e Ambientale, Politecnico di Milano, Italy)
Petra Bujňáková (Department of Structures and Bridges, Faculty of Civil Engineering, University of Žilina, Slovakia)
Anikó Borbála Csébfalvi (Department of Civil Engineering, Institute of Smart Technology and Engineering, Faculty of Engineering and Information Technology, University of Pécs, Hungary)
Mirjana S. Devetaković (Faculty of Architecture, University of Belgrade, Serbia)
Szabolcs Fischer (Department of Transport Infrastructure and Water Resources Engineering, Faculty of Architerture, Civil Engineering and Transport Sciences Széchenyi István University, Győr, Hungary)
Radomir Folic (Department of Civil Engineering, Faculty of Technical Sciences, University of Novi Sad Serbia)
Jana Frankovská (Department of Geotechnics, Faculty of Civil Engineering, Slovak University of Technology in Bratislava, Slovakia)
János Gyergyák (Department of Architecture and Urban Planning, Institute of Architecture, Faculty of Engineering and Information Technology, University of Pécs, Hungary)
Kay Hameyer (Chair in Electromagnetic Energy Conversion, Institute of Electrical Machines, Faculty of Electrical Engineering and Information Technology, RWTH Aachen University, Germany)
Elena Helerea (Dept. of Electrical Engineering and Applied Physics, Faculty of Electrical Engineering and Computer Science, Transilvania University of Brasov, Romania)
Ákos Hutter (Department of Architecture and Urban Planning, Institute of Architecture, Faculty of Engineering and Information Technolgy, University of Pécs, Hungary)
Károly Jármai (Institute of Energy and Chemical Machinery, Faculty of Mechanical Engineering and Informatics, University of Miskolc, Hungary)
Teuta Jashari-Kajtazi (Department of Architecture, Faculty of Civil Engineering and Architecture, University of Prishtina, Kosovo)
Róbert Kersner (Department of Technical Informatics, Institute of Information and Electrical Technology, Faculty of Engineering and Information Technology, University of Pécs, Hungary)
Rita Kiss (Biomechanical Cooperation Center, Faculty of Mechanical Engineering, Budapest University of Technology and Economics, Budapest, Hungary)
István Kistelegdi (Department of Building Structures and Energy Design, Institute of Architecture, Faculty of Engineering and Information Technology, University of Pécs, Hungary)
Stanislav Kmeť (President of University Science Park TECHNICOM, Technical University of Kosice, Slovakia)
Imre Kocsis (Department of Basic Engineering Research, Faculty of Engineering, University of Debrecen, Hungary)
László T. Kóczy (Department of Information Sciences, Faculty of Mechanical Engineering, Informatics and Electrical Engineering, University of Győr, Hungary)
Dražan Kozak (Faculty of Mechanical Engineering, Josip Juraj Strossmayer University of Osijek, Croatia)
György L. Kovács (Department of Technical Informatics, Institute of Information and Electrical Technology, Faculty of Engineering and Information Technology, University of Pécs, Hungary)
Balázs Géza Kövesdi (Department of Structural Engineering, Faculty of Civil Engineering, Budapest University of Engineering and Economics, Budapest, Hungary)
Tomáš Krejčí (Department of Mechanics, Faculty of Civil Engineering, Czech Technical University in Prague, Czech Republic)
Jaroslav Kruis (Department of Mechanics, Faculty of Civil Engineering, Czech Technical University in Prague, Czech Republic)
Miklós Kuczmann (Department of Automations, Faculty of Mechanical Engineering, Informatics and Electrical Engineering, Széchenyi István University, Győr, Hungary)
Tibor Kukai (Department of Engineering Studies, Institute of Smart Technology and Engineering, Faculty of Engineering and Information Technology, University of Pécs, Hungary)
Maria Jesus Lamela-Rey (Departamento de Construcción e Ingeniería de Fabricación, University of Oviedo, Spain)
János Lógó (Department of Structural Mechanics, Faculty of Civil Engineering, Budapest University of Technology and Economics, Hungary)
Carmen Mihaela Lungoci (Faculty of Electrical Engineering and Computer Science, Universitatea Transilvania Brasov, Romania)
Frédéric Magoulés (Department of Mathematics and Informatics for Complex Systems, Centrale Supélec, Université Paris Saclay, France)
Gabriella Medvegy (Department of Interior, Applied and Creative Design, Institute of Architecture, Faculty of Engineering and Information Technology, University of Pécs, Hungary)
Tamás Molnár (Department of Visual Studies, Institute of Architecture, Faculty of Engineering and Information Technology, University of Pécs, Hungary)
Ferenc Orbán (Department of Mechanical Engineering, Institute of Smart Technology and Engineering, Faculty of Engineering and Information Technology, University of Pécs, Hungary)
Zoltán Orbán (Department of Civil Engineering, Institute of Smart Technology and Engineering, Faculty of Engineering and Information Technology, University of Pécs, Hungary)
Dmitrii Rachinskii (Department of Mathematical Sciences, The University of Texas at Dallas, Texas, USA)
Chro Radha (Chro Ali Hamaradha) (Sulaimani Polytechnic University, Technical College of Engineering, Department of City Planning, Kurdistan Region, Iraq)
Maurizio Repetto (Department of Energy “Galileo Ferraris”, Politecnico di Torino, Italy)
Zoltán Sári (Department of Technical Informatics, Institute of Information and Electrical Technology, Faculty of Engineering and Information Technology, University of Pécs, Hungary)
Grzegorz Sierpiński (Department of Transport Systems and Traffic Engineering, Faculty of Transport, Silesian University of Technology, Katowice, Poland)
Zoltán Siménfalvi (Institute of Energy and Chemical Machinery, Faculty of Mechanical Engineering and Informatics, University of Miskolc, Hungary)
Andrej Šoltész (Department of Hydrology, Faculty of Civil Engineering, Slovak University of Technology in Bratislava, Slovakia)
Zsolt Szabó (Faculty of Information Technology and Bionics, Pázmány Péter Catholic University, Hungary)
Mykola Sysyn (Chair of Planning and Design of Railway Infrastructure, Institute of Railway Systems and Public Transport, Technical University of Dresden, Germany)
András Timár (Faculty of Engineering and Information Technology, University of Pécs, Hungary)
Barry H. V. Topping (Heriot-Watt University, UK, Faculty of Engineering and Information Technology, University of Pécs, Hungary)

POLLACK PERIODICA
Pollack Mihály Faculty of Engineering
Institute: University of Pécs
Address: Boszorkány utca 2. H–7624 Pécs, Hungary
Phone/Fax: (36 72) 503 650

E-mail: peter.ivanyi@mik.pte.hu

or amalia.ivanyi@mik.pte.hu

Indexing and Abstracting Services:

SCOPUS
CABELLS Journalytics

2023
Scopus
CiteScore	1.5
CiteScore rank	Q3 (Civil and Structural Engineering)
SNIP	0.849
Scimago
SJR index	0.288
SJR Q rank	Q3

Pollack Periodica
Publication Model	Hybrid
Submission Fee	none
Article Processing Charge	900 EUR/article
Printed Color Illustrations	40 EUR (or 10 000 HUF) + VAT / piece
Regional discounts on country of the funding agency	World Bank Lower-middle-income economies: 50% World Bank Low-income economies: 100%
Further Discounts	Editorial Board / Advisory Board members: 50% Corresponding authors, affiliated to an EISZ member institution subscribing to the journal package of Akadémiai Kiadó: 100%
Subscription fee 2025	Online subsscription: 381 EUR / 420 USD Print + online subscription: 456 EUR / 520 USD
Subscription Information	Online subscribers are entitled access to all back issues published by Akadémiai Kiadó for each title for the duration of the subscription, as well as Online First content for the subscribed content.
Purchase per Title	Individual articles are sold on the displayed price.