Uncertainty Analysis of Structural Dynamics by Using Two-Level Gaussian Processes

2011 ◽  
Author(s):  
Z. Xia ◽  
J. Tang
Keyword(s):  
Uncertainty Analysis ◽  
Gaussian Processes ◽  
Complex Structure ◽  
Element Model ◽  
Computer Code ◽  
Monte Carlo Sampling ◽  
High Fidelity ◽  
Structural Dynamic ◽  
Parameter Configuration ◽  
Gaussian Process Emulation

Uncertainty analysis is an important part of structural dynamic analysis in various applications. When a large complex structure is under consideration, component mode synthesis (CMS) is frequently used for reduced-order numerical analysis. But even so, in some situations the computational costs are still high for repeated running of a computer code which is required in uncertainty analysis. Gaussian processes offer an emulation approach to realization of fast sampling over a given parameter configuration space. However, both the low-fidelity data obtained by CMS and the corresponding sample obtained by Gaussian process emulation need to be assessed by comparing with high-fidelity data which can be obtained but are usually very expensive. When obvious bias exist in the low-fidelity data, two-level Gaussian processes are introduced for processing both the low- and high-fidelity data simultaneously to make more accurate predictions of quantities of interest. CMS can serve not only to provide low-fidelity data but also to locate problematic areas on complex structures. Comparisons of the results obtained by Monte Carlo sampling, which is performed using both a full finite element model and a CMS model, indicate that two-level Gaussian processes can be an efficient tool to emulate high-fidelity sampling with guaranteed accuracy.

Efficient Uncertainty Quantification in Structural Dynamic Analysis Using Two-Level Gaussian Processes

2015 ◽  
Author(s):  
Kai Zhou ◽  
Pei Cao ◽  
Jiong Tang
Keyword(s):  
Finite Element ◽  
Dynamic Analysis ◽  
Uncertainty Quantification ◽  
Large Scale ◽  
Computational Cost ◽  
Response Prediction ◽  
Element Model ◽  
High Fidelity ◽  
Structural Dynamic ◽  
Rapid Sampling

Uncertainty quantification is an important aspect in structural dynamic analysis. Since practical structures are complex and oftentimes need to be characterized by large-scale finite element models, component mode synthesis (CMS) method is widely adopted for order-reduced modeling. Even with the model order-reduction, the computational cost for uncertainty quantification can still be prohibitive. In this research, we utilize a two-level Gaussian process emulation to achieve rapid sampling and response prediction under uncertainty, in which the low- and high-fidelity data extracted from CMS and full-scale finite element model are incorporated in an integral manner. The possible bias of low-fidelity data is then corrected through high-fidelity data. For the purpose of reducing the emulation runs, we further employ Bayesian inference approach to calibrate the order-reduced model in a probabilistic manner conditioned on multiple predicted response distributions of concern. Case studies are carried out to validate the effectiveness of proposed methodology.

Characterization of Dynamic Response of Structures With Uncertainty by Using Gaussian Processes

2013 ◽  
Vol 135 (5) ◽  
Author(s):  
Z. Xia ◽  
J. Tang
Keyword(s):  
Uncertainty Analysis ◽  
Gaussian Processes ◽  
Dynamic Responses ◽  
Structural Dynamic ◽  
Design Assessment ◽  
Practical Applications ◽  
Credible Intervals ◽  
Efficient Data ◽  
Acquisition Costs ◽  
And Control

Characterizing dynamic characteristics of structures with uncertainty is an important task that provides critical predictive information for structural design, assessment, and control. In practical applications, sampling is the fundamental approach to uncertainty analysis but has to be conducted under various constraints. To address the frequently encountered data scarcity issue, in the present paper Gaussian processes are employed to predict and quantify structural dynamic responses, especially responses under uncertainty. A self-contained description of Gaussian processes is presented within the Bayesian framework with implementation details, and then a series of case studies are carried out using a cyclically symmetric structure that is highly sensitive to uncertainties. Structural frequency responses are predicted with data sparsely sampled within the full frequency range. Based on the inferred credible intervals, a measure is defined to quantify the potential risk of response maxima. Gaussian process emulation is proposed for Monte Carlo uncertainty analysis to reduce data acquisition costs. It is shown that Gaussian processes can be an efficient data-based tool for analyzing structural dynamic responses in the presence of uncertainty. Meanwhile, some technical challenges in the implementation of Gaussian processes are discussed.

Integrity Assessment of Damaged Flexible Pipe Cross-Sections

2014 ◽  
Author(s):  
Guomin Ji ◽  
Bernt J. Leira ◽  
Svein Sævik ◽  
Frank Klæbo ◽  
Gunnar Axelsson ◽  
...  
Keyword(s):  
Cross Sections ◽  
Three Dimensional ◽  
Element Model ◽  
Computer Code ◽  
Flexible Pipe ◽  
Dynamic Stresses ◽  
Integrity Assessment ◽  
Residual Capacity ◽  
Nonlinear Finite Element Model

This paper presents results from a case study performed to evaluate the residual capacity of a 6″ flexible pipe when exposed to corrosion damages in the tensile armour. A three-dimensional nonlinear finite element model was developed using the computer code MARC to evaluate the increase in mean and dynamic stresses for a given number of damaged inner tensile armor wires. The study also includes the effect of these damages with respect to the associated stresses in the pressure spiral. Furthermore, the implications of a sequence of wire failures with respect to the accumulated time until cross-section failure in a probabilistic sense are addressed.

Characterization of Nonlinear Coupled Dynamics in Sandwich Structures

2008 ◽  
Author(s):  
Ioannis T. Georgiou
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Geometric Nonlinearity ◽  
Sandwich Structures ◽  
Normal Modes ◽  
Element Model ◽  
Nonlinear Normal Modes ◽  
High Fidelity ◽  
Coupled Dynamics ◽  
Nonlinear Normal

In this work, the nonlinear coupled dynamics of a sandwich structure with hexagonal honeycomb core are characterized in terms of Proper Orthogonal Decomposition modes. A high fidelity nonlinear finite element model is derived to describe geometric nonlinearity and displacement and rotation fields that govern the coupled dynamics. Contrary to equivalent continuum models used to predict vibration properties of lattice and sandwich structures, a high fidelity finite element model allows for a quite detailed description of the distributed complicated geometric nonlinearity of the core. It was found that the free dynamics excited by a blast load and the forced dynamics excited by a harmonic force posses POD modes which are localized in space and time. The processing of the simulated dynamics by the Time Discrete Proper Transform forms a means to study the nonlinear coupled dynamics of sandwich structures in the context of nonlinear normal modes of vibration and reduced order models.

Stochastic Dynamic Analysis of Structures with Spatially Uncertain Material Parameters

2014 ◽  
Vol 14 (08) ◽  
pp. 1440029 ◽  
Author(s):  
Kheirollah Sepahvand ◽  
Steffen Marburg
Keyword(s):  
Finite Element ◽  
Modal Analysis ◽  
Polynomial Chaos ◽  
Element Model ◽  
Stochastic Dynamic ◽  
Stochastic Field ◽  
Structural Dynamic ◽  
Material Parameters ◽  
Material Uncertainties ◽  
Stochastic Dynamic Analysis

This paper investigates the uncertainty quantification in structural dynamic problems with spatially random variation in material and damping parameters. Uncertain and locally varying material parameters are represented as stochastic field by means of the Karhunen–Loève (KL) expansion. The stiffness and damping properties of the structure are considered uncertain. Stochastic finite element of structural modal analysis is performed in which modal responses are represented using the generalized polynomial chaos (gPC) expansion. Knowing the KL expansions of the random parameters, the nonintrusive technique is employed on a set of random collocation points where the structure deterministic finite element model is executed to estimate the unknown coefficients of the polynomial chaos expansions. A numerical case study is presented for a cantilever beam with random Young's modulus involving spatial variation. The proportional damping constants are estimated from the experimental modal analysis. The expected value, standard deviation, and probability distribution of the random eigenfrequencies and the damping ratios are evaluated. The results show high accuracy compared to the Monte-Carlo (MC) simulations with 3000 realizations. It is also demonstrated that the eigenfrequencies and the damping ratios are equally affected from material uncertainties.

Effects of Noise on Measured Ritz Vectors

1997 ◽  
Author(s):  
David C. Zimmerman ◽  
Timothy T. Cao
Keyword(s):  
Structural Damage ◽  
Element Model ◽  
Mode Shapes ◽  
Structural Damage Detection ◽  
Structural Dynamic ◽  
Response Data ◽  
Statistical Variation ◽  
Ritz Vectors ◽  
Traditional Mode ◽  
Model Correlation

Abstract Ritz vectors offer many advantages over the traditional mode shapes in the areas of model reduction and structural dynamic simulation. Building upon the recent development of an experimental method to extract Ritz vectors from measured dynamic response data, these vectors were also demonstrated to offer great potential in the areas of finite element model correlation and structural damage detection. In this paper, a Monte Carlo simulation is performed to study the accuracy and stability of Ritz vectors extracted from this new procedure using noise corrupted response data. The statistical variation of Ritz parameters and modal parameters extracted from the same data is made to assess the sensitivity of Ritz vector extraction to measured noise.

Stiffness Model of the Armature Assembly in a Jet Pipe Pressure Servo Valve

2020 ◽  
Author(s):  
Yaobao Yin ◽  
Chengpeng He ◽  
Jing Li
Keyword(s):  
Finite Element ◽  
Complex Structure ◽  
Small Deformation ◽  
Element Model ◽  
Continuity Condition ◽  
The Finite Element Method ◽  
Servo Valve ◽  
Linear Elastic ◽  
Stiffness Model ◽  
Static Performance

Abstract The armature assembly of the jet pipe pressure servo valve plays an important role in connecting the torque motor and the jet pipe amplifier. A stiffness model of its complex structure is very necessary for analyzing the dynamic/static performance of the jet pipe pressure servo valve. At the present work, the component parts in the armature assembly are simplified into linear elastic beams. The simplified armature assembly is a fourfold statically indeterminate structure under the premise of small deformation. The unknown forces and moments are solved by using the section continuity condition as the additional supplement equation, and the functional relationship between the electromagnetic torque produced from the torque motor and the armature rotation angle /the nozzle displacement is derived based on the Castigliano's Theorem. The finite element model of the armature assembly is also established to calculate the deformation under different loads and different spring tube lengths. The simulated displacements with the finite element method are consistent with the theoretical results. The experimental results of the recovery pressure of the jet pipe valve verified the theoretical model. The proposed stiffness calculation method can be used as a reference for designing and optimizing the armature assembly in the jet pipe pressure servo valve.

Uncertainty analysis for diagnosis of radiation temperature using Monte-Carlo sampling

2012 ◽  
Vol 24 (10) ◽  
pp. 2351-2354
Author(s):  
宋天明 Song Tianming ◽  
李三伟 Li Sanwei ◽  
易荣清 Yi Rongqing ◽  
杨家敏 Yang Jiamin ◽  
江少恩 Jiang Shao’en
Keyword(s):  
Monte Carlo ◽  
Uncertainty Analysis ◽  
Monte Carlo Sampling ◽  
Radiation Temperature

Structural Analysis of Riveted Structures Using a New FE Modelling Technique

2010 ◽  
Author(s):  
Michele Ferracci ◽  
Francesco Vivio ◽  
Vincenzo Vullo
Keyword(s):  
Degrees Of Freedom ◽  
Complex Structure ◽  
Element Model ◽  
3D Models ◽  
Fatigue Behaviour ◽  
Fe Analysis ◽  
Structural Behaviour ◽  
Fe Modelling ◽  
Closed Form Solutions ◽  
Riveted Joints

A theoretical approach, in order to define the structural behaviour of riveted joints, is presented. The closed form solutions lead to the definition of a Rivet Element useful to FE models of multi-riveted structures. The objective is an accurate evaluation of the local stiffness of riveted joints in FE analysis, which is fundamental to perform a reliable simulation of multi-joint structures and, consequently, a good estimate of loads acting on connections; this makes it possible to introduce new general criteria allowing, for example, to predict fatigue behaviour. On the other hand, a low number of degrees of freedom is needed when several connections are present in a complex structure. The goal is to reach a reliable model of the rivet region which can be used as the basis to develop a Rivet Element in FE analysis. The proposed Rivet Element combines the precision in the simulation with a very limited number degrees of freedom in the finite element model of a complex structure having several rivets. In the present paper the structural behavior of two simple riveted specimens is investigated experimentally and numerically using a new Rivet Element. A comparison with a joint model performed with very refined non-linear 3D models of rivet and with experimental data is performed and a good agreement is shown.

A Method for FE Model Updating of Coupled Vibro-Acoustic Systems Using Constrained Optimization

2013 ◽  
Author(s):  
D. V. Nehete ◽  
S. V. Modak ◽  
K. Gupta
Keyword(s):  
Finite Element ◽  
Constrained Optimization ◽  
Model Updating ◽  
Numerical Study ◽  
Element Model ◽  
Rectangular Cavity ◽  
Mode Shapes ◽  
Fe Model ◽  
Structural Dynamic ◽  
Fe Model Updating

Finite element (FE) model updating is now recognized as an effective approach to reduce modeling inaccuracies present in an FE model. FE model updating has been researched and studied well for updating FE models of purely structural dynamic systems. However there exists another class of systems known as vibro-acoustics in which acoustic response is generated in a medium due to the vibration of enclosing structure. Such systems are commonly found in aerospace, automotive and other transportation applications. Vibro-acoustic FE modeling is essential for sound acoustic design of these systems. Vibro-acoustic system, in contrast to purely structural system, has not received sufficient attention from FE model updating perspective and hence forms the topic of present paper. In the present paper, a method for finite element model updating of coupled structural acoustic model, constituted as a problem of constrained optimization, is proposed. An objective function quantifying error in the coupled natural frequencies and mode shapes is minimized to estimate the chosen uncertain parameters of the system. The effectiveness of the proposed method is validated through a numerical study on a 3D rectangular cavity attached to a flexible panel. The material property and the stiffness of joints between the panel and rectangular cavity are used as updating parameters. Robustness of the proposed method under presence of noise is investigated. It is seen that the method is not only able to obtain a close match between FE model and corresponding ‘measured’ vibro-acoustic characteristics but is also able to estimate the correction factors to the updating parameters with reasonable accuracy.

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