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Stochastic Galerkin Model Updating of Randomly Distributed Parameters

Nizamiev, Kamil
http://rave.ohiolink.edu/etdc/view?acc_num=akron1302884328

Abstract Details

2011, Master of Science in Engineering, University of Akron, Civil Engineering.
In civil and mechanical engineering applications, intrinsic randomness always exists in loads, measurement noise and natural variability of structural materials. Numerical modeling techniques such as finite element and boundary element methods have been prevalently used in the design of complex engineering systems in many fields. However, such numerical models that use the average or mean design characteristics at best lead to a coarse representation of the real physical condition. The difference between numerical models and physical realities ultimately leads to significant errors in estimating structural responses and, therefore, negatively affects the reliability in subsequent engineering judgments. With the constant development of various stochastic expansion methods, it has become feasible to propagate the stochasticity through numerical simulation. Therefore, model updating with a consideration of uncertainties has recently been spotlighted. Current ways include but are not limited to a representation of uncertain parts as discrete random variables with corresponding statistical properties and appropriate distribution and a representation of other physical quantities such as bending rigidity, density, etc. as spatially varying parameters with certain correlation function. However, it has not been possible to reproduce the spatially varying material properties with practical and reasonable accuracy. In this research, it is assumed that uncertainties exist in the material properties of structures. A transition in model updating from deterministic ways to the novel stochastic way has been accomplished by integrating Galerkin models with the Karhunen-Loeve (KL) expansion technique. This allows for the quantification and discretization of uncertainties in both spatial and stochastic domains. Thus, a simple one-dimensional identification model has been developed by combining the KL expansion, the Galerkin model and Ritz approximations. The ultimate solution to updating parameters is determined by adjusting the spectrally decomposed set of random variables, statistical properties (e.g., mean and variance) and correlation coefficients associated with the stochastic nature of structural materials until the dynamic modal properties (e.g., natural frequencies and mode shapes) from the identification model agree with those from monitored structures. Studies were thoroughly conducted by substituting real experimental tests with high-order 3D finite element models to verify the stochastic Galerkin model updating method. Moreover, a robust and heuristic approach for optimization mechanisms has been employed. Comprehensive stochastic model updating results for possible combinations of KL truncation order, the correlation length, mean and variance were provided to verify the proposed methodology. The proposed stochastic Galerkin model updating technique presented in this work has a potential to significantly impact the current way of updating spatially distributed parameters in civil infrastructures by integrating new features into standard deterministic model updating techniques. The proposed methodology will directly benefit the current state of stochastic finite element model updating in engineering systems. It will also open new perspectives on problems such corrosion detection of reinforced concrete structures and other applications related to changes in material properties.
Gun Jin Yun, Dr. (Advisor)
Subramaniya Hariharan, Dr. (Committee Member)
David Roke, Dr. (Committee Member)
103 p.
Civil Engineering
Stochastic Finite Element Model Updating

Recommended Citations

Citations

  • Nizamiev, K. (2011). Stochastic Galerkin Model Updating of Randomly Distributed Parameters [Master's thesis, University of Akron]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=akron1302884328

    APA Style (7th edition)

  • Nizamiev, Kamil. Stochastic Galerkin Model Updating of Randomly Distributed Parameters. 2011. University of Akron, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=akron1302884328.

    MLA Style (8th edition)

  • Nizamiev, Kamil. "Stochastic Galerkin Model Updating of Randomly Distributed Parameters." Master's thesis, University of Akron, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=akron1302884328

    Chicago Manual of Style (17th edition)

akron1302884328
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© 2011, all rights reserved.
This open access ETD is published by University of Akron and OhioLINK.