Sierra et al 2022a - Revision history

Xmartinez: Xmartinez moved page Review 592257080692 to Sierra et al 2022a

2022-06-11T12:30:00Z

Xmartinez moved page Review 592257080692 to Sierra et al 2022a

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2022-06-11T12:29:34Z

Se han eliminado los abstracts del cuerpo del artículo por parte del equipo editorial

Psierra: /* Resumen */

2022-06-10T10:36:27Z

‎Resumen

Psierra at 10:32, 10 June 2022

2022-06-10T10:32:10Z

Psierra at 08:19, 10 June 2022

2022-06-10T08:19:59Z

Psierra at 08:15, 10 June 2022

2022-06-10T08:15:18Z

Psierra: Psierra moved page Draft Sierra 755961050 to Review 592257080692

2022-05-20T17:18:23Z

Psierra moved page Draft Sierra 755961050 to Review 592257080692

Psierra at 15:12, 13 May 2022

2022-05-13T15:12:29Z

Psierra at 14:46, 13 May 2022

2022-05-13T14:46:31Z

Psierra at 16:10, 12 May 2022

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−	~~==DAMAGE DETECTION IN A FIBER REINFORCED POLYMERS BASED TOWER OF A FLOATING OFFSHORE WIND AND TIDAL POWER PLATFORM USING STRUCTURAL DYNAMIC PARAMETERS==~~
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−	~~==Abstract==~~
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−	The development of offshore renewable energy structures is growing at a fast pace, and their maintenance will become critical in further years. Because steel corrosion on offshore structures is one of their highest maintenance cost, researchers are working to replace steel by Fibre Reinforced Polymers (FRP), due to their immunity to corrosion. This is done in the EU H2020 funded project FIBREGY, which also seeks improving maintenance costs by incorporating Structural Health Monitoring (SHM) strategies in the structure. A critical issue in SHM is the damage detection process, which is addressed in this paper. This study aims to characterize the dynamic behaviour of an offshore windmill FRP tower, and its evolution due the presence of structural damage. This analysis will be carried out using a Finite Element Model (FEM) model of the structure, and the Serial-Parallel mixing theory to characterize the material performance. A sensitivity analysis of the changes in the dynamic response of the tower (frequencies and modal shapes) produced by structural damage is carried out. This analysis will provide the optimum design variables and objective functions required by a damage detection algorithm. The algorithm is optimization based, since it converts the damage detection problem into a mathematical one, and finds the best design variables to minimize the objective function. The algorithm is also model based, as it uses the structural model to obtain the objective function for the proposed design variables. Finally, this work presents the analysis of potential damage scenario, in order to evaluate if the damage is effectively detected.
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−	~~==Resumen==~~
−
−	El desarrollo de estructuras de energía renovable en alta mar está creciendo a un ritmo acelerado y su mantenimiento será crítico en los próximos años. Debido a que la corrosión del acero en las estructuras marinas se lleva la mayor parte de los costos en matenimiento, los investigadores están trabajando para reemplazar este material por polímeros reforzados con fibra (FRP), debido a que son inmunes a la corrosión. Esto es el objetivo del proyecto financiado por el programa UE H2020, FIBREGY, que también busca mejorar los costos de mantenimiento al incorporar estrategias de Supervisión Estructural (SHM). Un tema crítico en SHM es el proceso de detección de daños, que se aborda en este documento. Este estudio tiene como objetivo caracterizar el comportamiento dinámico de la torre de FRP de un aerogenerador marino y su comportamiento ante la presencia de daños estructurales. Este análisis se llevará a cabo utilizando un Modelo de Elementos Finitos (FEM) de la estructura y la teoría de mezcla Serie-Paralelo para caracterizar el material. Se realiza un análisis de sensibilidad de los cambios en la respuesta dinámica de la torre (frecuencias y formas modales) producidos por daños estructurales. Este análisis proporcionará las variables de diseño óptimas y las funciones objetivo requeridas por un algoritmo de detección de daños. El algoritmo está basado en la optimización, ya que convierte el problema de detección de daños en uno matemático para encontrar las mejores variables de diseño que minimizen la función objetivo. Este también está basado en modelos, ya que utiliza el FEM para evaluar la función objetivo con las variables de diseño propuestas. Finalmente, este trabajo presenta el análisis de un caso dañado de referencia, con el fin de evaluar el método de detección de daño.
−
	==1 INTRODUCTION==		==1 INTRODUCTION==

@@ Line 39: / Line 39: @@
 ==Resumen==
-El desarrollo de estructuras de energía renovable en alta mar está creciendo a un gran ritmo y su mantenimiento será crítico en los próximos años. Debido a que la corrosión del acero en las estructuras marinas es el costo de mantenimiento más alto, los investigadores están trabajando para reemplazar este material por polímeros reforzados con fibra (FRP), debido a que son inmunes a la corrosión. En esto se trabaja en el proyecto financiado por la UE H2020 FIBREGY, que también busca mejorar los costos de mantenimiento al incorporar estrategias de Monitoreo de Salud Estructural (SHM) en la estructura. Un tema crítico en SHM es el proceso de detección de daños, que se aborda en este documento. Este estudio tiene como objetivo caracterizar el comportamiento dinámico de la torre de FRP de un aerogenerador marino y su evolución ante la presencia de daños estructurales. Este análisis se llevará a cabo utilizando un modelo de elementos finitos (FEM) de la estructura y la teoría de mezcla Serie-Paralelo para caracterizar el material. Se realiza un análisis de sensibilidad de los cambios en la respuesta dinámica de la torre (frecuencias y formas modales) producidos por daños estructurales. Este análisis proporcionará las variables de diseño óptimas y las funciones objetivo requeridas por el algoritmo de detección de daños. Este está basado en la optimización, ya que convierte el problema de detección de daños en matemático, encontrando las mejores variables de diseño que minimicen la función objetivo. El algoritmo también está basado en modelos, ya que utiliza el modelo numérico de la estructura para obtener la función objetivo a partir de las variables de diseño propuestas. Finalmente, este trabajo presenta el análisis de un potencial escenario de daño, con el fin de evaluar si el daño es detectado.
+El desarrollo de estructuras de energía renovable en alta mar está creciendo a un ritmo acelerado y su mantenimiento será crítico en los próximos años. Debido a que la corrosión del acero en las estructuras marinas se lleva la mayor parte de los costos en matenimiento, los investigadores están trabajando para reemplazar este material por polímeros reforzados con fibra (FRP), debido a que son inmunes a la corrosión. Esto es el objetivo del proyecto financiado por el programa UE H2020, FIBREGY, que también busca mejorar los costos de mantenimiento al incorporar estrategias de Supervisión Estructural (SHM). Un tema crítico en SHM es el proceso de detección de daños, que se aborda en este documento. Este estudio tiene como objetivo caracterizar el comportamiento dinámico de la torre de FRP de un aerogenerador marino y su comportamiento ante la presencia de daños estructurales. Este análisis se llevará a cabo utilizando un Modelo de Elementos Finitos (FEM) de la estructura y la teoría de mezcla Serie-Paralelo para caracterizar el material. Se realiza un análisis de sensibilidad de los cambios en la respuesta dinámica de la torre (frecuencias y formas modales) producidos por daños estructurales. Este análisis proporcionará las variables de diseño óptimas y las funciones objetivo requeridas por un algoritmo de detección de daños. El algoritmo está basado en la optimización, ya que convierte el problema de detección de daños en uno matemático para encontrar las mejores variables de diseño que minimizen la función objetivo. Este también está basado en modelos, ya que utiliza el FEM para evaluar la función objetivo con las variables de diseño propuestas. Finalmente, este trabajo presenta el análisis de un caso dañado de referencia, con el fin de evaluar el método de detección de daño.
 ==1 INTRODUCTION==

@@ Line 39: / Line 39: @@
 ==Resumen==
-El desarrollo de estructuras de energía renovable en alta mar está creciendo a un gran ritmo y su mantenimiento será crítico en los próximos años. Debido a que la corrosión del acero en las estructuras marinas es el costo de mantenimiento más alto, los investigadores están trabajando para reemplazar este material por polímeros reforzados con fibra (FRP), debido a que son inmunes a la corrosión. En esto se trabaja en el proyecto financiado por la UE H2020 FIBREGY, que también busca mejorar los costos de mantenimiento al incorporar estrategias de Monitoreo de Salud Estructural (SHM) en la estructura. Un tema crítico en SHM es el proceso de detección de daños, que se aborda en este documento. Este estudio tiene como objetivo caracterizar el comportamiento dinámico de la torre de FRP de un aerogenerador marino y su evolución ante la presencia de daños estructurales. Este análisis se llevará a cabo utilizando un modelo de elementos finitos (FEM) de la estructura y la teoría de mezcla Serie-Paralelo para caracterizar el material. Se realiza un análisis de sensibilidad de los cambios en la respuesta dinámica de la torre (frecuencias y formas modales) producidos por daños estructurales. Este análisis proporcionará las variables de diseño óptimas y las funciones objetivo requeridas por el algoritmo de detección de daños. Este está basado en la optimización, ya que convierte el problema de detección de daños en uno matemático y encuentra las mejores variables de diseño para minimizar la función objetivo. El algoritmo también está basado en modelos, ya que utiliza el modelo estructural para obtener la función objetivo para las variables de diseño propuestas. Finalmente, este trabajo presenta el análisis del escenario de daño potencial, con el fin de evaluar si el daño es efectivamente detectado.
+El desarrollo de estructuras de energía renovable en alta mar está creciendo a un gran ritmo y su mantenimiento será crítico en los próximos años. Debido a que la corrosión del acero en las estructuras marinas es el costo de mantenimiento más alto, los investigadores están trabajando para reemplazar este material por polímeros reforzados con fibra (FRP), debido a que son inmunes a la corrosión. En esto se trabaja en el proyecto financiado por la UE H2020 FIBREGY, que también busca mejorar los costos de mantenimiento al incorporar estrategias de Monitoreo de Salud Estructural (SHM) en la estructura. Un tema crítico en SHM es el proceso de detección de daños, que se aborda en este documento. Este estudio tiene como objetivo caracterizar el comportamiento dinámico de la torre de FRP de un aerogenerador marino y su evolución ante la presencia de daños estructurales. Este análisis se llevará a cabo utilizando un modelo de elementos finitos (FEM) de la estructura y la teoría de mezcla Serie-Paralelo para caracterizar el material. Se realiza un análisis de sensibilidad de los cambios en la respuesta dinámica de la torre (frecuencias y formas modales) producidos por daños estructurales. Este análisis proporcionará las variables de diseño óptimas y las funciones objetivo requeridas por el algoritmo de detección de daños. Este está basado en la optimización, ya que convierte el problema de detección de daños en matemático, encontrando las mejores variables de diseño que minimicen la función objetivo. El algoritmo también está basado en modelos, ya que utiliza el modelo numérico de la estructura para obtener la función objetivo a partir de las variables de diseño propuestas. Finalmente, este trabajo presenta el análisis de un potencial escenario de daño, con el fin de evaluar si el daño es detectado.
 ==1 INTRODUCTION==

← Older revision		Revision as of 08:19, 10 June 2022
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	The development of offshore renewable energy structures is growing at a fast pace, and their maintenance will become critical in further years. Because steel corrosion on offshore structures is one of their highest maintenance cost, researchers are working to replace steel by Fibre Reinforced Polymers (FRP), due to their immunity to corrosion. This is done in the EU H2020 funded project FIBREGY, which also seeks improving maintenance costs by incorporating Structural Health Monitoring (SHM) strategies in the structure. A critical issue in SHM is the damage detection process, which is addressed in this paper. This study aims to characterize the dynamic behaviour of an offshore windmill FRP tower, and its evolution due the presence of structural damage. This analysis will be carried out using a Finite Element Model (FEM) model of the structure, and the Serial-Parallel mixing theory to characterize the material performance. A sensitivity analysis of the changes in the dynamic response of the tower (frequencies and modal shapes) produced by structural damage is carried out. This analysis will provide the optimum design variables and objective functions required by a damage detection algorithm. The algorithm is optimization based, since it converts the damage detection problem into a mathematical one, and finds the best design variables to minimize the objective function. The algorithm is also model based, as it uses the structural model to obtain the objective function for the proposed design variables. Finally, this work presents the analysis of potential damage scenario, in order to evaluate if the damage is effectively detected.		The development of offshore renewable energy structures is growing at a fast pace, and their maintenance will become critical in further years. Because steel corrosion on offshore structures is one of their highest maintenance cost, researchers are working to replace steel by Fibre Reinforced Polymers (FRP), due to their immunity to corrosion. This is done in the EU H2020 funded project FIBREGY, which also seeks improving maintenance costs by incorporating Structural Health Monitoring (SHM) strategies in the structure. A critical issue in SHM is the damage detection process, which is addressed in this paper. This study aims to characterize the dynamic behaviour of an offshore windmill FRP tower, and its evolution due the presence of structural damage. This analysis will be carried out using a Finite Element Model (FEM) model of the structure, and the Serial-Parallel mixing theory to characterize the material performance. A sensitivity analysis of the changes in the dynamic response of the tower (frequencies and modal shapes) produced by structural damage is carried out. This analysis will provide the optimum design variables and objective functions required by a damage detection algorithm. The algorithm is optimization based, since it converts the damage detection problem into a mathematical one, and finds the best design variables to minimize the objective function. The algorithm is also model based, as it uses the structural model to obtain the objective function for the proposed design variables. Finally, this work presents the analysis of potential damage scenario, in order to evaluate if the damage is effectively detected.
		+
		+	==Resumen==
		+
		+	El desarrollo de estructuras de energía renovable en alta mar está creciendo a un gran ritmo y su mantenimiento será crítico en los próximos años. Debido a que la corrosión del acero en las estructuras marinas es el costo de mantenimiento más alto, los investigadores están trabajando para reemplazar este material por polímeros reforzados con fibra (FRP), debido a que son inmunes a la corrosión. En esto se trabaja en el proyecto financiado por la UE H2020 FIBREGY, que también busca mejorar los costos de mantenimiento al incorporar estrategias de Monitoreo de Salud Estructural (SHM) en la estructura. Un tema crítico en SHM es el proceso de detección de daños, que se aborda en este documento. Este estudio tiene como objetivo caracterizar el comportamiento dinámico de la torre de FRP de un aerogenerador marino y su evolución ante la presencia de daños estructurales. Este análisis se llevará a cabo utilizando un modelo de elementos finitos (FEM) de la estructura y la teoría de mezcla Serie-Paralelo para caracterizar el material. Se realiza un análisis de sensibilidad de los cambios en la respuesta dinámica de la torre (frecuencias y formas modales) producidos por daños estructurales. Este análisis proporcionará las variables de diseño óptimas y las funciones objetivo requeridas por el algoritmo de detección de daños. Este está basado en la optimización, ya que convierte el problema de detección de daños en uno matemático y encuentra las mejores variables de diseño para minimizar la función objetivo. El algoritmo también está basado en modelos, ya que utiliza el modelo estructural para obtener la función objetivo para las variables de diseño propuestas. Finalmente, este trabajo presenta el análisis del escenario de daño potencial, con el fin de evaluar si el daño es efectivamente detectado.

	==1 INTRODUCTION==		==1 INTRODUCTION==

@@ Line 387: / Line 387: @@
 Kucherenko, S. & Y. Sytsko (2005). Application of Deterministic Low-Discrepancy Sequences in Global Optimization. Computational Optimization and Applications 30, 297–318.
-Martinez, X., S. Oller, F. Rastellini, & A. Barbat (2008). A numerical procedure simulating RC structures reinforced with FRP using the serial/parallel mixing theory. Computers and
+Martinez, X., S. Oller, F. Rastellini, & A. Barbat (2008). A numerical procedure simulating RC structures reinforced with FRP using the serial/parallel mixing theory. Computers and Structures 86, 1604–1618.
-−
 Structures 86, 1604–1618.
 Powell, M. (2009). The BOBYQA Algorithm for Bound Constrained Optimization without Derivatives. Technical report, Department of Applied Mathematics and Theoretical Physics.

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 ===2.2 Material===
-The FRP used in the scaled tower is composed of a vinylester based resin with glass fiber reinforcement, with a <math display="inline">20 %</math> on volume participation. The main characteristics are listed in Tab 1. The composite has <math display="inline">6</math> layers of unidirectional fibres in the following orientations, angles from the axis of the tower, see Fig. 1. From external to internal layer: <math display="inline">0^{\circ }   /  55^{\circ }   /  0^{\circ }   /  {-55}^{\circ }   /  0^{\circ }   /  90^{\circ } </math>.
+The FRP used in the scaled tower is composed of a vinylester based resin with glass fibre reinforcement, with a <math display="inline">20 %</math> of fibre volume fraction. The main characteristics are listed in Tab 1. The composite has <math display="inline">6</math> layers of unidirectional fibres in the following orientations, from external to internal layer: [<math display="inline">0^{\circ }   /  55^{\circ }   /  0^{\circ }   /  {-55}^{\circ }   /  0^{\circ }   /  90^{\circ } </math>], angles from the axis of the tower, see Fig. 1. .
 {|  class="floating_tableSCP wikitable" style="text-align: center; margin: 1em auto;min-width:50%;"
 |+ style="font-size: 75%;" |<span id='table-1'></span>Table. 1 Materials properties
@@ Line 102: / Line 102: @@
 ===2.3 Numerical Analysis===
-A dynamic analysis of the model is done using an academic multi-physics FEM code, FEMUSS, developed by the International Centre for Numerical Methods in Engineering (CIMNE) and the Polytechnical University of Catalunya (UPC). The different orthotropic composite layers, are treated using the serial/parallel mixing theory, (Martinez, Oller, Rastellini, & Barbat 2008).
+A dynamic analysis of the model is done using an in-house multi-physics FEM code, FEMUSS, developed by the International Centre for Numerical Methods in Engineering (CIMNE) and the Polytechnical University of Catalunya (UPC). The different orthotropic composite layers, are treated using the Serial-Parallel mixing theory, (Martinez, et al. 2008).
 ===2.4 Damaged Case===
@@ Line 233: / Line 233: @@
 There <math display="inline">lb</math> and <math display="inline">ub</math> represents the lower and upper bound limit, respectively. The global optimization is referred to find the set of <math display="inline">\mathbf{x}</math> that minimize <math display="inline">f\mathbf{(x)}</math> over the entire feasible region. The problem is harder as the dimension <math display="inline">n</math> increases and, in cases when the behaviour of the objective function is unknown, is not possible to be certain whether one has found the true global optimum.
-Several global optimization algorithms were developed that are more or less efficient, depending on the behaviour of the problem. In this paper, the Multi Level Single Linkage (MLSL) algorithm for global optimization from the NLopt library, (Johnson 2020), is used for the damage detection problem. It consist of a sequence of local optimizations starting from random points, proposed by Rinnooy Kan & Timmer (1987a), (1987b). An alternative implementation is applied. This uses a Sobol low discrepancy sequence as starting points, instead of random numbers, providing more accurate results, practically and theoretically guaranteed. This application was presented by Kucherenko & Sytsko (2005). The local optimization is carried out by the derivative - free and bound - constrained BOBYQUA local optimizer. This algorithm was presented by Powell (2009). It consist of a quadratic approximation of the objective function, constructed iteratively.
+Several global optimization algorithms were developed that are more or less efficient, depending on the behaviour of the problem. In this paper, the Multi Level Single Linkage (MLSL) algorithm for global optimization from the NLopt library, (Johnson 2020), is used for the damage detection problem. It consist of a sequence of local optimizations starting from random points, proposed by Rinnooy Kan & Timmer (1987a), (1987b). An alternative implementation is applied and it uses a Sobol low discrepancy sequence as starting points, instead of random numbers, providing more accurate results, practically and theoretically guaranteed. This application was presented by Kucherenko & Sytsko (2005). The local optimization is carried out by the derivative - free and bound - constrained BOBYQUA local optimizer. This algorithm was presented by Powell (2009). It consist of a quadratic approximation of the objective function, constructed iteratively.
 ===4.2 Design variables===
@@ Line 275: / Line 275: @@
 |}
-At first, a simpler scenario is evaluated, where are only <math display="inline">10</math> design variables. Each one of these represents the <math display="inline">3</math> layers with <math display="inline">0^{\circ }</math> fibre orientation of <math display="inline">1</math> zone in the structure. Divided as shown in Fig 1. If, for example, the design variable <math display="inline">x_7 = 1</math>, it implies that the <math display="inline">3</math> layers <math display="inline">0^{\circ }</math> in zone <math display="inline">7</math> are damaged, so it's Young's modulus is equal to <math display="inline">100  MPa</math>. The damaged case, described in Section 2.4, is represented by the vector of Eq. 4.<span id="eq-4"></span>
+At first, a simpler scenario is evaluated, where are only <math display="inline">10</math> design variables. Each one of these represents the <math display="inline">3</math> layers with <math display="inline">0^{\circ }</math> fibre orientation of <math display="inline">1</math> zone in the structure, see Fig. 1. If, for example, the design variable <math display="inline">x_7 = 1</math>, it implies that the <math display="inline">3</math> layers <math display="inline">0^{\circ }</math> in zone <math display="inline">7</math> are damaged, so it's Young's modulus is equal to <math display="inline">100  MPa</math>. The damaged case, described in Section 2.4, is represented by the vector of Eq. 4.<span id="eq-4"></span>
 {| class="formulaSCP" style="width: 100%; text-align: left;"
 |-

@@ Line 35: / Line 35: @@
 ==Abstract==
-The development of offshore renewable energy structures is growing at a fast pace, and their maintenance will become critical in further years. Because steel corrosion on offshore structures is one of their highest maintenance cost, researchers are working to replace steel by Fibre Reinforced Polymers (FRP), due to their immunity to corrosion. This is done in the EU H2020 funded project FIBREGY, which also seeks improving maintenance costs by incorporating Structural Health Monitoring (SHM) strategies in the structure. A critical issue in SHM is the damage detection process, which is addressed in this paper. This study aims to characterize the dynamic behaviour of an offshore windmill FRP tower, and its evolution due the presence of structural damage. This analysis will be carried out using a FEM model of the structure, and the Serial-Parallel mixing theory to characterize the material performance. A sensitivity analysis of the changes in the dynamic response of the tower (frequencies and modal shapes) produced by structural damage is carried out. This analysis will provide the optimum design variables and objective functions required by a damage detection algorithm. The algorithm is optimization based, since it converts the damage detection problem into a mathematical one, and finds the best design variables to minimize the objective function. The algorithm is also model based, as it uses the structural model to obtain the objective function for the proposed design variables.Finally, this work presents the analysis of potential damage scenario, in order to evaluate if the damage is effectively detected.
+The development of offshore renewable energy structures is growing at a fast pace, and their maintenance will become critical in further years. Because steel corrosion on offshore structures is one of their highest maintenance cost, researchers are working to replace steel by Fibre Reinforced Polymers (FRP), due to their immunity to corrosion. This is done in the EU H2020 funded project FIBREGY, which also seeks improving maintenance costs by incorporating Structural Health Monitoring (SHM) strategies in the structure. A critical issue in SHM is the damage detection process, which is addressed in this paper. This study aims to characterize the dynamic behaviour of an offshore windmill FRP tower, and its evolution due the presence of structural damage. This analysis will be carried out using a Finite Element Model (FEM) model of the structure, and the Serial-Parallel mixing theory to characterize the material performance. A sensitivity analysis of the changes in the dynamic response of the tower (frequencies and modal shapes) produced by structural damage is carried out. This analysis will provide the optimum design variables and objective functions required by a damage detection algorithm. The algorithm is optimization based, since it converts the damage detection problem into a mathematical one, and finds the best design variables to minimize the objective function. The algorithm is also model based, as it uses the structural model to obtain the objective function for the proposed design variables. Finally, this work presents the analysis of potential damage scenario, in order to evaluate if the damage is effectively detected.
 ==1 INTRODUCTION==
-Offshore renewable energy is a cornerstone of the clean energy transition in the EU. It consists of many different sources that are abundant, natural and clean, obtaining energy from wind, wave and tidal. This can be harnessed by modern technologies without emitting any greenhouse gases, (European Commission 2020). There is no doubt that the offshore renewable energy exploitation has a large potential to grow. But, the open sea is a very aggressive environment, which may largely affect the maintenance costs of the installations and therefore the overall cost of offshore energy generation. The owners of offshore assets are aware of that and are paying a steep price. A massive amount of steel goes into those assets, and all this metal is subject to degradation, which explains why corrosion accounts for approximately 60% of offshore maintenance costs. In order to address this problem, the main objective of the EU H2020 952966 project FIBREGY, (EU 2023), is enabling the extensive use of FRP materials in the structure of the next generation of large Offshore Wind and Tidal Power (OWTP) platforms, due to the convenient immunity to corrosion and superior fatigue performance of these materials. Another innovative aspect that will be considered is the use of multifunctional FRP materials in the OWTP structure, by embedding sensors in the material for continuous Structural Health Monitoring (SHM).
+Offshore renewable energy is a cornerstone of the clean energy transition in the EU. It consists of many different sources that are abundant, natural and clean, obtaining energy from wind, wave and tidal. This can be harnessed by modern technologies without emitting any greenhouse gases, (European Commission 2020). There is no doubt that the offshore renewable energy exploitation has a large potential to grow. However, the open sea is a very aggressive environment, which may largely affect the maintenance costs of the installations and therefore the overall cost of offshore energy generation. The owners of offshore assets are aware of that and are paying a steep price. A massive amount of steel goes into those assets, and all this metal is subject to degradation, which explains why corrosion accounts for approximately 60% of offshore maintenance costs. In order to address this problem, the main objective of the EU H2020 952966 FIBREGY project, (EU 2023), is enabling the extensive use of FRP materials in the structure of the next generation of large Offshore Wind and Tidal Power (OWTP) platforms, due to the convenient immunity to corrosion and superior fatigue performance of these materials. Another innovative aspect that will be considered is the use of multifunctional FRP materials in the OWTP structure, by embedding sensors in the material for continuous SHM.
-During FIBREGY project, a scale (1:50) of an FRP tower with an embedded SHM system will be tested. In this paper, a dynamic numerical analysis of this scaled structure is carried out. A Finite Element Model (FEM) is made and analysed to obtain its dynamic behaviour, characterized by frequencies and modal shapes. Also, a model updating and optimization based damage detection method is proposed for this structure and tested using a numerical damaged scenario.
+During FIBREGY project, a scale (1:50) of an FRP tower with an embedded SHM system will be tested. In this paper, a dynamic numerical analysis of this scaled structure is carried out. A FEM is made and analysed to obtain its dynamic behaviour, characterized by frequencies and modal shapes. Also, a model updating and optimization based damage detection method is proposed for this structure and tested using a numerical damaged scenario.
 ==2 Numerical Model==
@@ Line 64: / Line 64: @@
 |}
-The FEM design is done with GiD,(CIMNE 2020), a pre and post processor for numerical simulations in science and engineering. The structure is discretized in <math display="inline">54\,096</math> nodes and <math display="inline">46\,080</math> hexahedra linear elements and is shown in Fig. 2.
+The FEM design is done with GiD,(CIMNE 2020), a pre and post processor for numerical simulations in science and engineering. The structure is discretized in <math display="inline">54\,096</math> nodes and <math display="inline">46\,080</math> hexahedra linear elements and, as it is shown in Fig. 2.
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 ==3 Dynamic behaviour==
-The embedded SHM system that is going to be used in tests allows up to <math display="inline">1\,000 \  Hz</math> of sampling rate. In consequence, the analysis is limited to <math display="inline">500 \ Hz</math>, the half of the sampling rate value, corresponding to the Nyquist frequency.
+The embedded SHM system that is going to be used in tests allows up to <math display="inline">1\,000 \  Hz</math> of sampling rate. In consequence, the analysis is limited to <math display="inline">500 \ Hz</math>, the half of the sampling rate value, corresponding to the Nyquist frequency. This value defines the bandwith by Fourier transform based analysis.
 In this range, <math display="inline">7</math> modes were found. The frequency values obtained in the analysis of the undamaged scenario and the described damaged reference case, are listed and compared in Tab. 2. Due to the rotational symmetry of the structure, modes 1-2, 3-4 and 6-7 have almost the same values between them, but not equal because the asymmetry in the fibre's orientation. These are flexural modes, while mode 5 is expansive, as is shown in Figs. 3 and 4. There, dark blue colour represents no displacement, red biggest displacement.
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-In this paper Eigenfrequencies Method is used. The natural frequencies of the structure are very sensitive to the damage and it is easy to implement a monitoring system, thus is widely used. The variations in the frequencies and which mode is more or less affected depends on the position and severity of the damage. But it represents the global behavior of the structure, since doesn't use spatial information. The proposed objective function is Eq. 6.<span id="eq-6"></span>
+In this paper the Eigenfrequencies Method is used. The natural frequencies of the structure are very sensitive to the damage and it is easy to implement a monitoring system, thus is widely used. The variations in the frequencies and which mode is more or less affected depends on the position and severity of the damage. But it represents the global behavior of the structure, since doesn't use spatial information. The proposed objective function is Eq. 6.<span id="eq-6"></span>
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 In the first scenario, with <math display="inline">10</math> design variables as explained before, the optimization process is set up with a limit of <math display="inline">1\,000</math> evaluations. In that range, the algorithm found a minimum in the evaluation <math display="inline">255</math>, with an objective function value of <math display="inline">0.088</math>. The evolution of the objective function value is shown in Fig. 6.
-The design variables of that minima are listed in Eq. 9 and plotted in the histogram of Fig. 6. Except for minimal differences in zones <math display="inline">2</math> and <math display="inline">10</math> (less than <math display="inline">2  %</math>), the obtained structure and the damaged case are equal, so the damage is found.<span id="eq-9"></span>
+The design variables corresponding with the obtained minimum are listed in Eq. 9 and plotted in the histogram of Fig. 6. Except for minimal differences in zones <math display="inline">2</math> and <math display="inline">10</math> (less than <math display="inline">2  %</math>), the obtained structure and the damaged case are equal, so the damage is found.<span id="eq-9"></span>
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-In the <math display="inline">60</math> design variables scenario, the optimization is limited to <math display="inline">3\,500</math> evaluations. In this scenario the minimum value of the objective function was found in the evaluation <math display="inline">2\,801</math>, with an objective function value of <math display="inline">1.148</math>. The evolution of this function and the histogram representing the best sample found are shown in Fig. 7.
+In the <math display="inline">60</math> design variables scenario, the optimization is limited to <math display="inline">3\,500</math> evaluations. In this scenario the minimum value of the objective function was found in the evaluation <math display="inline">2\,801</math>, with an objective function value of <math display="inline">1.148</math>. Although this value is bigger than the obtained before, is acceptable, due the problem is harder to solve. The evolution of this function and the histogram representing the best sample found are shown in Fig. 7.
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 In this paper a numerical model of offshore windmill FRP tower is presented and its dynamic behaviour is characterized by its natural frequencies and modal shapes. A reference damaged case of the tower is analysed. The sensitivity to damage of the natural vibration frequencies of the structure has been verified.
-Also, a damage detection method is presented, based on optimization algorithms and model updating techniques. This method includes detection, localization and extension of the damage.  Based on the comparison of the natural frequencies, <math display="inline">2</math> cases are evaluated with different space discretization. At first one, with the structure divided into <math display="inline">10</math> zones to apply damage, while in the second scenario into <math display="inline">60</math> zones. In both, satisfactory results were obtained. It was demonstrated that the proposed damage detection method could be used in SHM for this kind of structures.
+Also, a damage detection method is presented, based on optimization algorithms and model updating techniques. This method includes detection, localization and extension of the damage.  Based on the comparison of the natural frequencies, <math display="inline">2</math> cases are evaluated with different space discretization. One with the structure divided into <math display="inline">10</math> zones to apply damage, while in the second scenario into <math display="inline">60</math> zones. In both, satisfactory results were obtained. Its demonstrated that the proposed damage detection method could be used in SHM process for this kind of structures. These monitoring strategies periodically evaluates possibles structural damages, improving the operational safety of the structure and reducing its maintenance costs.
 ==6 Acknowledgments==