Open Access
Inertia transfer concept based general method for the determination of the base inertial parameters
(Springer, 2015) Ros Ganuza, Javier; Plaza Puértolas, Aitor; Iriarte Goñi, Xabier; Aginaga García, Jokin; Ingeniería; Ingeniaritza; Institute of Smart Cities - ISC
This paper presents a new algorithm to obtain the symbolic expressions of any of the possible base inertial parameter sets of a multibody system. Based on the ¿inertia transfer concept¿, a procedure is proposed to write a system of equations from which the base parameters are obtained. This leads to an automatizable and general method to obtain these parameters symbolically. The method can also be used to determine base inertial parameters numerically, and it can be even more straightforward to implement and use than the standard numerical methods. An example is presented to illustrate in detail the application of the algorithm, and to compare its results with those of a standard numerical procedure. The symbolic base inertial parameters can be of interest in symbolic simplification of the dynamic equations for real-time applications, design optimization, dynamic parameter identification, model reduction, and in other fields.
Open Access
Dataset for the identification of a ultra-low frequency multidirectional energy harvester for wind turbines
(Elsevier, 2024-11-20) Bacaicoa Díaz, Julen; Hualde Otamendi, Mikel; Merino Olagüe, Mikel; Plaza Puértolas, Aitor; Iriarte Goñi, Xabier; Castellano Aldave, Jesús Carlos; Carlosena García, Alfonso; Ingeniería Eléctrica, Electrónica y de Comunicación; Ingeniaritza Elektrikoa, Elektronikoa eta Telekomunikazio Ingeniaritza; Ingeniería; Ingeniaritza; Institute of Smart Cities - ISC; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
This paper presents a publicly available dataset designed to support the identification (characterization) and performance optimization of an ultra-low-frequency multidirectional vibration energy harvester. The dataset includes detailed measurements from experiments performed to fully characterize its dynamic behaviour. The experimental data encompasses both input (acceleration)-output (energy) relationships, as well as internal system dynamics, measured using a synchronized image processing and signal acquisition system. In addition to the raw input-output data, the dataset also provides post-processed information, such as the angular positions of the moving masses, their velocities and accelerations, derived from recorded high-speed videos at 240 Hz. The dataset also includes the measured power output generated in the coils. This dataset is intended to enable further research on vibration energy harvesters by providing experimental data for identification, model validation, and performance optimization, particularly in the context of energy harvesting in low-frequency and multidirectional environments, such as those encountered in wind turbines.
Open Access
Hybrid modelling and identification of mechanical systems using Physics-Enhanced Machine Learning
(Elsevier, 2025-11-15) Merino Olagüe, Mikel; Iriarte Goñi, Xabier; Castellano Aldave, Jesús Carlos; Plaza Puértolas, Aitor; Ingeniería; Ingeniaritza; Institute of Smart Cities - ISC; Ingeniería Eléctrica, Electrónica y de Comunicación; Ingeniaritza Elektrikoa, Elektronikoa eta Telekomunikazio Ingeniaritza; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
Obtaining mathematical models for mechanical systems is a key subject in engineering. These models are essential for calculation, simulation and design tasks, and they are usually obtained from physical principles or by fitting a black-box parametric input-output model to experimental data. However, both methodologies have some limitations: physics based models may not take some phenomena into account and black-box models are complicated to interpretate. In this work, we develop a novel methodology based on discrepancy modelling, which combines physical principles with neural networks to model mechanical systems with partially unknown or unmodelled physics. Two different mechanical systems with partially unknown dynamics are successfully modelled and the values of their physical parameters are obtained. Furthermore, the obtained models enable numerical integration for future state prediction, linearization and the possibility of varying the values of the physical parameters. The results show how a hybrid methodology provides accurate and interpretable models for mechanical systems when some physical information is missing. In essence, the presented methodology is a tool to obtain better mathematical models, which could be used for analysis, simulation and design tasks.
Open Access
Mode-displacement method for structural dynamic analysis of bio-inspired structures: a palm-tree stem subject to wind effects
(Taylor & Francis, 2022) Plaza Puértolas, Aitor; Vargas Silva, Gustavo Adolfo; Iriarte Goñi, Xabier; Ros Ganuza, Javier; Ingeniería; Ingeniaritza
Biological materials (orthotropic materials), like wood, can offer good mechanical properties with a minimum amount of material, making their internal structure the suitable one to be applied on bio-inspired structures. The knowledge of the exceptional structural performance of palm trees, and specially its response to different loading conditions, provides useful information when lightweight structures with high slenderness ratio are desired. Recent researches focused on the analysis of palm trees subject to static loading conditions, ignoring the fluctuating nature of the wind speed. The purpose of this study is to simulate in a computational efficient way the effect of dynamic loading conditions applied on palm trees. Using the mode displacement method, the number of degrees of freedom of a dynamic finite element analysis can be drastically reduced with a minimal loss of accuracy. It was applied to simulate the behavior of structures comprised of an orthotropic material subject to a stochastic dynamic load. The influence of the number of selected degrees of freedom has also been studied. In addition, an exponential integration method is proposed to perform the time integration procedure. The results obtained show that a properly reduced model suitably represents the full finite element model without any appreciable loss of accuracy; it is also shown that computational cost can be drastically reduced. This method could give an appropriate computational representation of the behavior of orthotropic structures, and it could be used for studying more complex bio-inspired structures.
Open Access
Ultra-low frequency multidirectional harvester for wind turbines
(Elsevier, 2023) Castellano Aldave, Jesús Carlos; Carlosena García, Alfonso; Iriarte Goñi, Xabier; Plaza Puértolas, Aitor; Ingeniería; Ingeniería Eléctrica, Electrónica y de Comunicación; Institute of Smart Cities - ISC; Ingeniaritza; Ingeniaritza Elektrikoa, Elektronikoaren eta Telekomunikazio Ingeniaritzaren; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
In this paper we propose, and demonstrate through a prototype, a completely novel device able to harvest mechanical energy from the multidirectional vibrations in a wind turbine, and convert it into electrical, to power autonomous sensors. The application is very challenging since vibrations are of ultra-low frequency, well below 1 Hz, with accelerations of tenths of cm/s2 (0.01 g), and the device must capture energy from the movement in any direction. According to our experiments, the device is capable to generate average powers around the milliwatt in the operation conditions of a wind turbine, which are enough for some very-low power sensor nodes, or at least to considerably extend the life-time of batteries. The device is based on the principle of moving (inertial) masses comprised of magnets in Hallbach arrays interacting with coils, and can work for movements on any direction of a plane. To the best of our knowledge, this is the first device specifically proposed for wind turbines and one of the few that work in such low frequencies, and capture energy from movements on any direction on a plane. Only three harvesters proposed in the literature, intended for distinct applications, can work at such low frequencies, and our device exhibits a better efficiency. Though comparisons with harvesters working in different contexts and, even using different conversion principles, is not completely fair, we make in this paper a comparison to the closest ones, resorting to two different figures of merit.
Open Access
Triaxial accelerometer based azimuth estimator for horizontal axis wind turbines
(Elsevier, 2023) Plaza Puértolas, Aitor; Ros Ganuza, Javier; Gainza González, Gorka; Fuentes Lárez, José David; Ingeniería; Ingeniaritza; Institute of Smart Cities - ISC; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
One of the elements that receives the greatest stresses is the main shaft. Its damage is directly related to the cyclical nature of its rotational motion. However, the vast majority of horizontal axis wind turbines (HAWT) do not have sensors to measure the main-shaft angular position (azimuth), or they are not always easily accessible. Using a main-shaft placed single triaxial accelerometer for the estimation of the azimuth is proposed as a low intrusion approach that can be easily deployed in machines already in use. An approach using a tandem of two extended Kalman filters (calibration/prediction), aiming for a precise and robust estimation, is presented. The estimator is able to calibrate for accelerometer positional and orientation errors, as well as for bias drift. To simplify the burden of deployment, a simple procedure is proposed to determine the covariance matrices for a particular HAWT from those determined in a synthetic case. The proposed approach is analyzed using synthetic data, OpenFAST simulation of NREL-5MW HAWT. It outperforms the ATAN naive approach by an order of magnitude, showing errors smaller than 0.4o. The filter shows a good behavior, coherent with that of the synthetic setup, when tested on experimental data obtained from a 3MW HAWT.
Open Access
Modelado simbólico para la simulación en tiempo real de sistemas multicuerpo
(2016) Plaza Puértolas, Aitor; Ros Ganuza, Javier; Ingeniería Mecánica, Energética y de Materiales; Mekanika, Energetika eta Materialen Ingeniaritza
Esta tesis se sitúa dentro del contexto de los métodos simbólicos en la dinámica de sistemas multicuerpo y recoge la experiencia de 25 años en este contexto. La situación anterior a la tesis era la de una librería simbólica C++ que permitía plantear las ecuaciones dinámicas de la mecánica pero con ciertas limitaciones. La más importante posiblemente eran los grandes tiempos de ejecución para la generación de las ecuaciones del sistemas dinámico (código en C que luego se compila para obtener un ejecutable) que incluso para problemas simples podía tardar horas. Además, la exportación de las ecuaciones dinámicas no era óptima en el número de operaciones. El doctorando ha estado involucrado en diversos proyectos de investigación, en uno de ellos (el más demandante respecto a las ecuaciones dinámicas) se modelaba una locomotora de ferrocarril, que tardaba en general las ecuaciones dinámicas unos 8000s y se necesitaba MAPLE para optimizar las ecuaciones, ya que no eran muy óptimas. Después de la tesis el tiempo de generar las ecuaciones es 800s y el número de operaciones del código generado es el 50% y MAPLE no es necesario. Estas cifras son extrapolables a otros problemas. El estado del arte en multicuerpo simbólico son los trabajos de J.C. Samin y P. Fisette, al menos en lo que se refiere a publicaciones, aunque J. McPhee ha colaborado en la creación de MapleSym, que es un motor simbólico de renombre. Hay también otros trabajos como el sofware NewEuler 2C y 2M. Los más avanzados son los que utilizan formulaciones recursivas, pero están limitados por la implementación que ellos realizan en su software y por el tipo de coordenadas. En esta tesis doctoral se ha desarrollado un algebra de operadores y estructuras de datos de la dinámica que permiten la implementación de cualquier formalismo con cualquier tipo de coordenadas y obtener unas ecuaciones simbólicas muy óptimas. Con lo cual se eliminan las limitaciones del formalismo y del tipo de coordenadas. Esto presenta innumerables ventajas. Además, los tiempos computacionales y la calidad del código generado es similar al de estos que tomamos como referencia. Finalmente, se presenta un algoritmo que evitaría la aparición de expresiones susceptibles de simplificación trigonométrica, que es uno de los problemas más graves en la generación de ecuaciones simbólicas óptimas. Para ello, se propone un nuevo algebra de vectores, denominados extendidos, que pasa desapercibida al usuario, y que permitiría la generación de código más óptimo, más rápido y con menores recursos de memoria. Todos los demás algoritmos simbólicos existentes en un momento u otro requieren simplificar trigonométricamente si quieren obtener expresiones lo más óptimas posibles.
Open Access
Comprehensive analysis of rotor edgewise whirling mode interaction with rotor speed harmonics
(IOP Publishing, 2024) Torres Elizondo, Antonio; Gil Soto, Javier; Plaza Puértolas, Aitor; Aginaga García, Jokin; Ingeniería; Ingeniaritza; Institute of Smart Cities - ISC
This paper presents a model that investigates the interaction between rotor edgewise whirling modes and rotor speed harmonics in wind turbines. The model is based on kinematic and dynamic principles, with a focus on the multi-blade coordinate transformation, which is critical for simulating the behaviour of the rotor whirling modes in wind turbines. The research has two objectives: to investigate the interaction between the rotor edgewise whirling modes and the rotor speed harmonics, and to provide clearer graphs that explain the complex nature of this non-intuitive rotor dynamics. The paper concludes by highlighting the practical implications of the research findings, in particular the effectiveness of visualisation techniques in identifying and explaining unexpected interactions.
Open Access
A unified analytical disk cam profile generation methodology using the Instantaneous Center of Rotation for educational purpose
(Elsevier, 2024) Iriarte Goñi, Xabier; Bacaicoa Díaz, Julen; Plaza Puértolas, Aitor; Aginaga García, Jokin; Ingeniería; Ingeniaritza; Institute of Smart Cities - ISC; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
Cam design is a fundamental part of the Mechanism and Machine Theory (MMT) and is included in the vast majority of MMT books. Cam profile design is usually determined with graphical and analytical methods. Graphical methods are didactically very successful to introduce the theory of cam profile generation in a simple way. In turn, analytical methods allow computer implementations of cam profile generation in order to reproduce it accurately. Most modern MMT books describe analytical methods using geometric equations and envelope theory. However, the analytical profile definition depends on the specific type of follower and there is a lack of a general formulation. This work presents a unified and general analytical formulation for the disk cam profile determination. Based on the Instantaneous Center of Rotation and the kinematic inversion, the formulation provides analytical expressions of the cam profile and is applicable to any type of follower. Thus, the unified formulation can be used in forthcoming books on this discipline.
Open Access
A directivity correction for accurate semi-empirical wind turbine noise prediction
(IOP Publishing, 2024) Saldaña Barroso, Oier; Rautmann, C.; Plaza Puértolas, Aitor; Ingeniería; Ingeniaritza
Public acceptance of wind farms is a significant challenge in the development of wind energy. The acoustic impact generated by wind turbines is a common concern among local residents. The primary noise source in wind turbines is generated by aerodynamics. Atmospheric turbulence reaching the blade leading edge or turbulent boundary layer passing the trailing edge produce the main aeroacoustic sources. The noise generated by these mechanisms is commonly predicted by means of semi-empirical models, which do not demonstrate great reliability when compared to acoustic measurements. This paper presents a correction to the directivity of airfoil noise radiation, resulting in improved sound pressure levels on the ground plane surrounding a wind turbine. This improvement is achieved without requiring any additional computational effort. The sound pressure levels perceived on the ground plane are known to have asymmetrical shape. Maximum noise levels correspond to observers directly in the upwind and downwind locations, whereas the minimum levels belong to the positions close to the rotor plane. Said asymmetrical shape is not represented in the semi-empirical models. The proposed correction takes into consideration the airfoil thickness in the radiation directivity equations, resulting in the expected asymmetrical shape of noise footprints on the ground plane around a wind turbine. The correction was found to not affect the accuracy of the spectrum predicted by the semi-empirical models when compared to dedicated field measurements under the standard IEC 61400-11 procedure. When implementing the proposed correction, the virtual NREL 5 MW wind turbine's published noise footprints, which were originally calculated using computationally expensive methods, are accurately reproduced.