Real time parameter identification and solution reconstruction from experimental data using the Proper Generalized Decomposition

Some industrial processes are modelled by parametric partial differential equations. Integrating computational modelling and data assimilation into the control process requires obtaining a solution of the numerical model at the characteristic frequency of the process (real-time). This paper introduces a computational strategy allowing to efficiently exploit measurements of those industrial processes, providing the solution of the model at the required frequency. This is particularly interesting in the framework of control algorithms that rely on a model involving a set of parameters. For instance, the curing process of a composite material is modelled as a thermo-mechanical problem whose corresponding parameters describe the thermal and mechanical behaviours. In this context, the information available (measurements) is used to update the parameters of the model and to produce new values of the control variables (data assimilation). The methodology presented here is devised to ensure the possibility of having a response in real-time of the problem and therefore the capability of integrating it in the control scheme. The Proper Generalized Decomposition is used to describe the solution in the multi-parametric space. The real-time data assimilation requires a further simplification of the solution representation that better fits the data (reconstructed solution) and it provides an implicit parameter identification. Moreover, the analysis of the assimilated data sensibility with respect to the points where the measurements are taken suggests a criterion to locate the sensors

A finite element approach for the acoustic modelling of perforated dissipative mufflers with non-homogeneous properties

[EN] In this work, a finite element approach is presented for modeling sound propagation in perforated dissipative mufflers with non-homogeneous properties. The spatial variations of the acoustic properties can arise, for example, from uneven filling processes during manufacture and degradation associated with the flow of soot particles within the absorbent material. First, the finite element method is applied to the wave equation for a propagation medium with variable properties (outer chamber with absorbent material) and a homogeneous medium (central passage). For the case of a dissipative muffler, the characterization of the absorbent material is carried out by means of its equivalent complex density and speed of sound. To account for the spatial variations of these properties, a coordinate-dependent function is proposed for the filling density of the absorbent material. The coupling between the outer chamber and the central passage is achieved by using the acoustic impedance of the perforated central pipe, that relates the acoustic pressure jump and the normal velocity through the perforations. The acoustic impedance of the perforated central duct includes the influence of the absorbent material and therefore a spatial variation of the impedance is also taken into account. A detailed study is then presented to assess the influence of the heterogeneous properties and the perforated duct porosity on the acoustic attenuation performance of the muffler.The authors gratefully acknowledge the financial support of Ministerio de Ciencia e Innovacion and the European Regional Development Fund by means of the projects DPI2007-62635 and DPI2010-15412.Antebas, A.; Denia Guzmán, FD.; Pedrosa Sanchez, AM.; Fuenmayor Fernández, FJ. (2013). A finite element approach for the acoustic modelling of perforated dissipative mufflers with non-homogeneous properties. Mathematical and Computer Modelling. 57(7):1970-1978. https://doi.org/10.1016/j.mcm.2012.01.021S1970197857

Improved railway wheelset-track interaction model in the high-frequency domain

[EN] As it is well known, there are various phenomena related to railway train-track interaction, some of them caused by the high frequency dynamics of the system, such as rolling noise when the vehicle runs over the track, as well as squeal noise and short-pitch rail corrugation for curved tracks. Due to these phenomena and some others unsolved so far, a large effort has been made over the last 40 years in order to define suitable models to study the train-track interaction. The introduction of flexibility in wheelset and rail models was required to have a more realistic representation of the wheel-rail interaction effects at high frequencies. In recently published train-track interaction models, the rails are modelled by means of Timoshenko beam elements, valid up to 1.5 kHz for lateral rail vibration and up to 2 kHz for vertical vibration. This confines the frequency range of validity for the complete train-track model to 1.5 kHz. With the purpose of extending the range of validity above 1.5 kHz, a 3D track model based on the Moving Element Method (MEM) is developed in this paper to replace the Timoshenko beam considered in earlier studies, adopting cyclic boundary conditions and Eulerian coordinates. The MEM approach considers a mobile Finite Element (FE) mesh which moves with the vehicle, so the mass of the rail flows with the vehicle speed but in the opposite direction through the mesh. Therefore, the MEM permits to fix the contact area in the middle of a finitely long track and to refine the mesh only around the contact area, where the forces and displacements will be more significant. Additionally, a modal approach is adopted in order to reduce the number of degrees of freedom of the rail model. Both strategies lower substantially the computational cost. Simulation results are presented and discussed for different excitation sources including random rail roughness and singularities such as wheel flats. All the simulation cases are carried out for a Timoshenko beam and a 3D MEM track model in order to point out the differences in the contact forces above the range of validity of the Timoshenko beam.The authors gratefully acknowledge the financial support of Ministerio de Economía y Competitividad and the European Regional Development Fund (project TRA2013-45596-C2-1-R), as well as Generalitat Valenciana (project Prometeo/2012/023) and Ministerio de Educación, Cultura y Deporte (project SP20140659) as part of Programa Campus de Excelencia Internacional.Martínez Casas, J.; Giner Navarro, J.; Baeza González, LM.; Denia Guzmán, FD. (2017). Improved railway wheelset-track interaction model in the high-frequency domain. Journal of Computational and Applied Mathematics. 309(1):642-653. https://doi.org/10.1016/j.cam.2016.04.034S642653309

Acoustic modelling of exhaust devices with nonconforming finite element meshes and transfer matrices

[EN] Transfer matrices are commonly considered in the numerical modelling of the acoustic behaviour associated with exhaust devices in the breathing system of internal combustion engines, such as catalytic converters, particulate filters, perforated mufflers and charge air coolers. In a multidimensional finite element approach, a transfer matrix provides a relationship between the acoustic fields of the nodes located at both sides of a particular region. This approach can be useful, for example, when one-dimensional propagation takes place within the region substituted by the transfer matrix. As shown in recent investigations, the sound attenuation of catalytic converters can be properly predicted if the monolith is replaced by a plane wave four-pole matrix. The finite element discretization is retained for the inlet/outlet and tapered ducts, where multidimensional acoustic fields can exist. In this case, only plane waves are present within the capillary ducts, and three-dimensional propagation is possible in the rest of the catalyst subcomponents. Also, in the acoustic modelling of perforated mufflers using the finite element method, the central passage can be replaced by a transfer matrix relating the pressure difference between both sides of the perforated surface with the acoustic velocity through the perforations. The approaches in the literature that accommodate transfer matrices and finite element models consider conforming meshes at connecting interfaces, therefore leading to a straightforward evaluation of the coupling integrals. With a view to gaining flexibility during the mesh generation process, it is worth developing a more general procedure. This has to be valid for the connection of acoustic subdomains by transfer matrices when the discretizations are nonconforming at the connecting interfaces. In this work, an integration algorithm similar to those considered in the mortar finite element method, is implemented for nonmatching grids in combination with acoustic transfer matrices. A number of numerical test problems related to some relevant exhaust devices are then presented to assess the accuracy and convergence performance of the proposed procedure.Authors gratefully acknowledge the financial support of Ministerio de Ciencia e Innovacion and the European Regional Development Fund by means of the Projects DPI2007-62635 and DPI2010-15412.Denia, F.; Martínez-Casas, J.; Baeza, L.; Fuenmayor, F. (2012). Acoustic modelling of exhaust devices with nonconforming finite element meshes and transfer matrices. Applied Acoustics. 73(8):713-722. https://doi.org/10.1016/j.apacoust.2012.02.003S71372273

Study of railway curve squeal in the time domain using a high-frequency vehicle/track interaction model

[EN] Railway curve squeal is an intense tonal and annoying type of noise commonly attributed to self-excited vibrations during curving. The mechanisms for its generation remain unclear and it is still a subject of discussion among researchers. Most of them have considered the falling behaviour of the friction coefficient with the slip velocity essential for reenergising the system. Recently, some authors have found that squeal can also appear even for constant friction coefficient through the wheel modal coupling between the normal and tangential directions caused by the wheel/rail contact. This paper particularly evaluates whether the latter mechanism is sufficient to find squeal in curving conditions. The introduction of flexibility in the railway subsystems is required to widen the domain to the high-frequency range in which squeal occurs. One single flexible and rotatory wheelset is considered and suitable forces are prescribed at the primary suspension seats in the current investigation. The rails are modelled through the Moving Element Method (MEM), permitting to extend the range of validity of beam models usually utilised in the literature. This work extends the formulation to rails supported by a viscoelastic Winkler bedding. Both wheelset and track models are coupled by means of a non-linear and unsteady wheel/rail contact model based on Kalker¿s Variational Theory. Simulation results for different track curvatures and friction coefficients are presented and discussed, showing tonal peaks in the tangential contact forces of the inner wheel. These results can be associated with squeal according to the characterisation of this phenomenon, indicating that squeal can be found in curving conditions using advanced dynamic interaction models even with constant friction coefficient.The authors gratefully acknowledge the financial support of Spanish Ministry of Economy, Industry and Competitiveness and the European Regional Development Fund (project TRA2017-84701-R), as well as Generalitat Valenciana (project Prometeo/2016/007) and European Commission through the project "RUN2Rail - Innovative RUNning gear soluTiOns for new dependable, sustainable, intelligent and comfortable RAIL vehicles" (Horizon 2020 Shift2Rail JU call 2017, grant number 777564).Giner Navarro, J.; Martínez Casas, J.; Denia, FD.; Baeza González, LM. (2018). Study of railway curve squeal in the time domain using a high-frequency vehicle/track interaction model. Journal of Sound and Vibration. 431:177-191. https://doi.org/10.1016/j.jsv.2018.06.004S17719143

Acoustic behaviour of elliptical mufflers with single-inlet and double-outlet

Expansion chambers with single-inlet and double-outlet are used in the exhaust system of internal combustion engines since they provide noise attenuation similar to simple chambers (single inlet/outlet), and reduce the flow noise and back pressure. This work presents a detailed analysis of the acoustic attenuation performance of elliptical expansion chambers with single-inlet and double-outlet. First, the finite element method (FEM) is considered in order to obtain a reference solution. Then, the mode-matching method (MMM) is applied at the area discontinuities of the muffler, considering a circular inlet pipe, a central elliptical chamber and two circular outlet pipes. This method reduces the computational requirements and enables to couple the acoustic fields within each region, described by means of Mathieu functions in the elliptical chamber and Bessel functions in the circular pipes. The solution given by this analytical approach is compared with finite element results and experimental measurements for a selected configuration, showing a good agreement. The acoustic behaviour is then analysed in detail as a function of the chamber length, the . eccentricity of the elliptical cross-section and the position of the inlet and outlet pipes. Some potential means to improve the acoustic performance are proposed

A multidimensional analytical study of sound attenuation in catalytic converters

In this work, a multidimensional analytical model is presented for the sound attenuation assessment of axisymmetric catalytic converters. Bessel functions are considered for the circular ducts, while spherical Hankel and Legendre functions are used for the expansion/contraction tapered ducts. Two alternative modelling techniques are implemented and compared for the monolith: (1) An equivalent bulk reacting absorbent material, in which the wave propagation is determined by the effective complex and frequency dependent density and speed of sound; (2) A coupling approach between both sides of the ceramic monolith in which a plane wave transfer matrix is considered, therefore retaining only onedimensional propagation within the capillary ducts. Benchmarking of the developed analytical techniques with finite element calculations shows good agreement. The influence of several parameters on the sound attenuation of the catalyst is investigated

A model of a rotating railway wheel for the prediction of sound radiation

The axial symmetry of a railway wheel is taken into account to expand its vibrational response around the circumferential direction using Fourier series. This allows the vibroacoustic problem of the wheel to be formulated in a two-dimensional frame, solving for the dynamic and acoustic variables analytically in the circumferential direction. By adopting an Eulerian approach, the inertial effects associated with the rotation of the wheelset are included in the model, assuming a constant angular speed of rotation. To represent a railway wheelset, the wheel is constrained at the inner edge of the hub and the contribution of the rigid body motion of the wheelset is superimposed on its response. The latter is evaluated analytically under the assumption of small rigid body displacements. The computational efficiency of the proposed methodology is found to be three orders of magnitude greater than a full three-dimensional methodology, without compromising the accuracy. The results are compared in terms of acoustic radiation with the commercial package Ansys, showing similar sound power levels in almost all the frequency range apart from some differences at low frequencies due to the use of an acoustic model based on radiation ratios