Uncertainty quantification of dynamic responses in the frequency domain in the context of virtual testing

2015 ◽  
Vol 342 ◽  
pp. 303-329 ◽  
Author(s):  
Maik Brehm ◽  
Arnaud Deraemaeker
Keyword(s):  
Uncertainty Quantification ◽  
Frequency Domain ◽  
Dynamic Responses ◽  
Virtual Testing

scholarly journals Methods for the Calculation of Thermoacoustic Stability Margins and Monte Carlo-Free Uncertainty Quantification

2017 ◽  
Author(s):  
Georg A. Mensah ◽  
Luca Magri ◽  
Jonas P. Moeck
Keyword(s):  
Monte Carlo ◽  
Factor Analysis ◽  
Risk Factor ◽  
Uncertainty Quantification ◽  
Frequency Domain ◽  
Gas Turbines ◽  
Network Models ◽  
System Stability ◽  
Risk Factor Analysis ◽  
Model Parameters

Thermoacoustic instabilities are a major threat for modern gas turbines. Frequency-domain based stability methods, such as network models and Helmholtz solvers, are common design tools because they are fast compared to compressible CFD computations. Frequency-domain approaches result in an eigenvalue problem, which is nonlinear with respect to the eigenvalue. Nonlinear functions of the frequency are, for example, the n–τ model, impedance boundary conditions, etc. Thus, the influence of the relevant parameters on mode stability is only given implicitly. Small changes in some model parameters, which are obtained by experiments with some uncertainty, may have a great impact on stability. The assessment of how parameter uncertainties propagate to system stability is therefore crucial for safe gas turbine operation. This question is addressed by uncertainty quantification. A common strategy for uncertainty quantification in thermoacoustics is risk factor analysis. It quantifies the uncertainty of a set of parameters in terms of the probability of a mode to become unstable. One general challenge regarding uncertainty quantification is the sheer number of uncertain parameter combinations to be quantified. For instance, uncertain parameters in an annular combustor might be the equivalence ratio, convection times, geometrical parameters, boundary impedances, flame response model parameters etc. Assessing also the influence of all possible combinations of these parameters on the risk factor is a numerically very costly task. A new and fast way to obtain algebraic parameter models in order to tackle the implicit nature of the eigenfrequency problem is using adjoint perturbation theory. Though adjoint perturbation methods were recently applied to accelerate the risk factor analysis, its potential to improve the theory has not yet been fully exploited. This paper aims to further utilize adjoint methods for the quantification of uncertainties. This analytical method avoids the usual random Monte Carlo simulations, making it particularly attractive for industrial purposes. Using network models and the open-source Helmholtz solver PyHoltz it is also discussed how to apply the method with standard modeling techniques. The theory is exemplified based on a simple ducted flame and a combustor of EM2C laboratory for which experimental validation is available.

Dynamic Response of 3D Surface/Embedded Rigid Foundations of Arbitrary Shapes on Multi-Layered Soils in Time Domain

2019 ◽  
Vol 19 (09) ◽  
pp. 1950106 ◽  
Author(s):  
Zejun Han ◽  
Mi Zhou ◽  
Xiaowen Zhou ◽  
Linqing Yang
Keyword(s):  
Dynamic Response ◽  
Frequency Domain ◽  
Time Domain ◽  
Dynamic Stiffness ◽  
Dynamic Responses ◽  
Rigid Foundation ◽  
Layered Soils ◽  
Stiffness Matrices ◽  
The Time Domain ◽  
Arbitrary Shapes

Significant differences between the predicted and measured dynamic response of 3D rigid foundations on multi-layered soils in the time domain were identified due to the existence of uncertainties, which makes the issue a complicated one. In this study, a numerical method was developed to determine the dynamic responses of 3D rigid surfaces and embedded foundations of arbitrary shapes that are bonded to a multi-layered soil in the time domain. First, the dynamic stiffness matrices of the rigid foundations in the frequency domain are calculated via integral domain transformation. Secondly, a dynamic stiffness equation for rigid foundations in the time domain is established via the mixed variables formulation, which is based on the discrete dynamic stiffness matrices in the frequency domain. The proposed method can be applied to the treatment of systems with multiple degrees of freedom without losing the true information that concerns the coupling characteristics. Numerical examples are presented to demonstrate the accuracy of the proposed method for predicting the horizontal, vertical, rocking, and torsional vibrations. Further, a parametric study was carried out to provide insight into the dynamic behavior of the soil–foundation interaction (SFI) while considering soil nonhomogeneity. The results indicate that the elastic modulus of the soil has a significant impact on the dynamic responses of the rigid foundation. Finally, a numerical example of a rigid foundation resting on a six-layered, semi-infinite soil demonstrates that the proposed method can be used to deal with multi-layered media in the time domain in a relatively easy way.

Uncertainty Quantification Using Streamline Based Inversion and Distance Based Clustering

2015 ◽  
Vol 138 (1) ◽  
Author(s):  
Jihoon Park ◽  
Jeongwoo Jin ◽  
Jonggeun Choe
Keyword(s):  
Uncertainty Quantification ◽  
Travel Time ◽  
History Matching ◽  
Reservoir Characterization ◽  
Uncertainty Assessment ◽  
Dynamic Responses ◽  
Time Inversion ◽  
Dynamic Data ◽  
Reservoir Models ◽  
Permeability Distribution

For decision making, it is crucial to have proper reservoir characterization and uncertainty assessment of reservoir performances. Since initial models constructed with limited data have high uncertainty, it is essential to integrate both static and dynamic data for reliable future predictions. Uncertainty quantification is computationally demanding because it requires a lot of iterative forward simulations and optimizations in a single history matching, and multiple realizations of reservoir models should be computed. In this paper, a methodology is proposed to rapidly quantify uncertainties by combining streamline-based inversion and distance-based clustering. A distance between each reservoir model is defined as the norm of differences of generalized travel time (GTT) vectors. Then, reservoir models are grouped according to the distances and representative models are selected from each group. Inversions are performed on the representative models instead of using all models. We use generalized travel time inversion (GTTI) for the integration of dynamic data to overcome high nonlinearity and take advantage of computational efficiency. It is verified that the proposed method gathers models with both similar dynamic responses and permeability distribution. It also assesses the uncertainty of reservoir performances reliably, while reducing the amount of calculations significantly by using the representative models.

scholarly journals Analysis and optimization of the effects of frictional and viscous dampers on dynamical systems

2019 ◽  
Vol 38 (2) ◽  
pp. 255-269
Author(s):  
Marlon Wesley Machado Cunico ◽  
Jennifer Desiree Medeiros Cavalheiro
Keyword(s):  
Frequency Domain ◽  
Degrees Of Freedom ◽  
Transfer Functions ◽  
Mechanical Systems ◽  
Static Friction ◽  
Coulomb Force ◽  
Dynamic Responses ◽  
Dynamical Response ◽  
Viscous Dampers ◽  
Three Degrees Of Freedom

Over the last several years, the complexity of products has been increasing in parallel to the product cost thus becoming one of main focal points for development. On the other hand, although several applications struggle to fix vibration problems, highlighting the importance of damper design, literature that compares the benefits and disadvantages between of dry-frictional, viscous, and Coulomb–viscous dampers is still rare. Owing to this, the main goal of this work is to present a study that compares the dynamical response of mechanical systems against several damper types. For this research, we analyzed the effects of three types of damper (viscous, Coulomb–viscous, and dry-frictional dampers) on two mechanical systems. The first system consists of a mass-spring-damper with one degree of freedom, while the second system is a rotational machine with three degrees of freedom. The sensibility analyses of each damper were also studied, where the viscosity, Coulomb force, static friction, and Stribeck decay were the variables. In this work, mechanical systems were studied in a forced vibration condition and analyzed in the time and frequency domain in addition to identifying the main transfer functions in the frequency domain. In this analysis, the displacement, receptance, and force reaction were considered to be the study responses. After analyzing the main effect of damper coefficients on the general dynamic responses, we performed an optimization study in order to evidence the optimal configurations of either majorly viscous or frictional damper. Lastly, we analyzed the main behavior of this optimized damper on three-degrees-of-freedom rotational dynamic system.

scholarly journals Zero and root loci of disturbed spring–mass systems

2014 ◽  
Vol 470 (2164) ◽  
pp. 20130751 ◽  
Author(s):  
Christophe Lecomte
Keyword(s):  
Complex Systems ◽  
Frequency Domain ◽  
Dynamic Responses ◽  
Local Disturbance ◽  
Broad Category ◽  
Analytical Properties ◽  
Discrete Values ◽  
Atomic Lattices ◽  
Elliptical Region

Models consisting of chains of particles that are coupled to their neighbours appear in many applications in physics or engineering, such as in the study of dynamics of mono-atomic and multi-atomic lattices, the resonances of crystals with impurities and the response of damaged bladed discs. Analytical properties of the dynamic responses of such disturbed chains of identical springs and masses are presented, including when damping is present. Several remarkable properties in the location of the resonances (poles) and anti-resonances (zeros) of the displacements in the frequency domain are presented and proved. In particular, it is shown that there exists an elliptical region in the frequency–disturbance magnitude plane from which zeros are excluded and the discrete values of the frequency and disturbance at which double poles occur are identified. A particular focus is on a local disturbance, such as when a spring or damper is modified at or between the first and last masses. It is demonstrated how, notably through normalization, the techniques and results of the paper apply to a broad category of more complex systems in physics, chemistry and engineering.

scholarly journals FRICTIONAL EFFECTS ON THE DYNAMIC RESPONSES OF A SINGLE-STAGE SPUR GEAR SYSTEMS

2021 ◽  
Vol 03 (02) ◽  
pp. 191-203
Author(s):  
Tareq Z HAMAD ◽  
Khaldoon F. BRETHEE ◽  
Ghalib R IBRAHIM
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Spur Gear ◽  
Industrial Applications ◽  
Single Stage ◽  
Dynamic Responses ◽  
Mechanical Equipment ◽  
Gear Mesh ◽  
The Time Domain ◽  
Complex Matter

Gears are paramout rotary mechanical equipment as its used in many industrial applications, for example in cars, industrial compressors and other applications. Therefore, monitoring the development of its condition is very important to prevent the aggravation of defects and stopping production. Friction between gears is causes of vibration but its representation in modeling and the analysis of its effect on the dynamic response is a very complex matter. In this study, the friction effect was studied by relying on equal load sharing formula and by relying on the sliding velocity direction of single-stage spur gears. The time domain was converted to the frequency domain, depending on the Fast Fourier Transform ( FFT ) method. Dynamic modeling results indicate that the friction between gears has a significant effect on the Vibration response of gearbox. This effect can be noticed by increasing the vibration amplitude in the time domain. It can also be seen by increasing the gear mesh frequency (GMF) amplitude and by increasing the amplitude of its harmonics in the frequency domain.

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