scholarly journals An efficient inverse method for structural identification considering modeling and response uncertainties

2021 ◽  
Author(s):  
Lixiong Cao ◽  
Jie Liu ◽  
Cheng Lu ◽  
Wei Wang
Keyword(s):  
Inverse Problem ◽  
Inverse Problems ◽  
Dimension Reduction ◽  
Inverse Method ◽  
Structural Parameters ◽  
Computational Cost ◽  
Structural Parameter ◽  
High Dimensional Model Representation ◽  
Response Uncertainty ◽  
Convex Model

Abstract The inverse problem analysis method provides an effective way for the structural parameter identification. Due to the coupling of multi-source uncertainties in the measured responses and the modeling parameters, the inverse of unknown structural parameter will face the challenges in the solving mechanism and the computational cost. In this paper, an uncertain inverse method based on convex model and dimension reduction decomposition is proposed to realize the interval identification of unknown structural parameter according to the uncertain measured responses and modeling parameters. Firstly, the polygonal convex set model is established to quantify the uncertainties of modeling parameters. Afterwards, a space collocation method based on dimension reduction decomposition is proposed to transform the inverse problem considering multi-source uncertainties into a few interval inverse problems considering response uncertainty. The transformed interval inverse problem involves the two-layer solving process including interval propagation and optimization updating. In order to solve the interval inverse problems considering response uncertainty, an efficient interval inverse method based on the high dimensional model representation and affine algorithm is further developed. Through the coupling of the above two methods, the proposed uncertain inverse method avoids the time-consuming multi-layer nested calculation procedure, and then effectively realize the inverse uncertainty quantification of unknown structural parameters. Finally, two engineering examples are provided to verify the effectiveness of the proposed uncertain inverse method.

Uncertainty quantification in Bayesian inverse problems with model and data dimension reduction

Geophysics ◽  
2019 ◽  
Vol 84 (6) ◽  
pp. M15-M24 ◽  
Author(s):  
Dario Grana ◽  
Leandro Passos de Figueiredo ◽  
Leonardo Azevedo
Keyword(s):  
Inverse Problem ◽  
Inverse Problems ◽  
Dimension Reduction ◽  
Uncertainty Quantification ◽  
Computational Cost ◽  
Nonlinear Inverse Problems ◽  
Reduction Methods ◽  
Nonlinear Elastic ◽  
Elastic Inversion ◽  
The Impact

The prediction of rock properties in the subsurface from geophysical data generally requires the solution of a mathematical inverse problem. Because of the large size of geophysical (seismic) data sets and subsurface models, it is common to reduce the dimension of the problem by applying dimension reduction methods and considering a reparameterization of the model and/or the data. Especially for high-dimensional nonlinear inverse problems, in which the analytical solution of the problem is not available in a closed form and iterative sampling or optimization methods must be applied to approximate the solution, model and/or data reduction reduce the computational cost of the inversion. However, part of the information in the data or in the model can be lost by working in the reduced model and/or data space. We have focused on the uncertainty quantification in the solution of the inverse problem with data and/or model order reduction. We operate in a Bayesian setting for the inversion and uncertainty quantification and validate the proposed approach in the linear case, in which the posterior distribution of the model variables can be analytically written and the uncertainty of the model predictions can be exactly assessed. To quantify the changes in the uncertainty in the inverse problem in the reduced space, we compare the uncertainty in the solution with and without data and/or model reduction. We then extend the approach to nonlinear inverse problems in which the solution is computed using an ensemble-based method. Examples of applications to linearized acoustic and nonlinear elastic inversion allow quantifying the impact of the application of reduction methods to model and data vectors on the uncertainty of inverse problem solutions. Examples of applications to linearized acoustic and nonlinear elastic inversion are shown.

scholarly journals Structural Parameter Identification of Fixed End Beams by Inverse Method Using Measured Natural Frequencies

2008 ◽  
Vol 15 (5) ◽  
pp. 505-515 ◽  
Author(s):  
T. Türker ◽  
A. Bayraktar
Keyword(s):  
Differential Equation ◽  
Parameter Identification ◽  
Inverse Method ◽  
Natural Frequencies ◽  
Structural Parameters ◽  
Added Mass ◽  
Modal Testing ◽  
Dynamic Responses ◽  
Structural Parameter ◽  
Fixed End

Structural parameter identification based on the measured dynamic responses has become very popular recently. This paper presents structural parameter identification of fixed end beams by inverse method using measured natural frequencies. An added mass is used as a modification tool. The measurements of the flexural vibrations of a fixed end beam with and without added mass are performed by using experimental modal testing. The solution of free bending transverse vibration of the beam is obtained by solving the differential equation motion of Bernoulli-Euler beam. By introducing the natural frequencies from experimental measurements into the solution of differential equation, the structural parameters of the fixed end beam are calculated.It is seen from the results that the values of the mass distribution and elasticity modulus identified using the first natural frequency of the beam nearly close to the real values. Besides, the theoretical frequencies obtained using the identified structural parameters also close to the measured frequencies.

Uncertainty quantification in stochastic inversion with dimensionality reduction using variational autoencoder

Geophysics ◽  
2021 ◽  
pp. 1-65
Author(s):  
Mingliang Liu ◽  
Dario Grana ◽  
Leandro Passos de Figueiredo
Keyword(s):  
Inverse Problem ◽  
Inverse Problems ◽  
Dimensionality Reduction ◽  
Dimension Reduction ◽  
Uncertainty Quantification ◽  
Generative Models ◽  
Stochastic Inversion ◽  
Variational Autoencoder ◽  
Reduction Methods ◽  
The Impact

Estimating rock and fluid properties in the subsurface from geophysical measurements is a computationally and memory intensive inverse problem. For nonlinear problems with non-Gaussian variables, analytical solutions are generally not available, and the solutions of those inverse problems must be approximated using sampling and optimization methods. To reduce the computational cost, model and data can be re-parameterized into low-dimensional spaces where the solution of the inverse problem can be computed more efficiently. Among the potential dimensionality reduction methods, deep learning algorithms based on deep generative models provide an efficient approach to reduce the dimension of the model and data vectors. However, such dimension reduction might lead to information loss in the reconstructed model and data, reduction of the accuracy and resolution of the inverted models, and under or overestimation of the uncertainty of the predicted models. To comprehensively investigate the impact of model and data dimension reduction with deep generative models on uncertainty quantification, we compare the prediction uncertainty in nonlinear inverse problem solutions obtained from Markov chain Monte Carlo and ensemble-based data assimilation methods implemented in lower dimensional data and model spaces using a deep variational autoencoder. The proposed workflow is applied to two geophysical inverse problems for the prediction of reservoir properties: pre-stack seismic inversion and seismic history matching. The inversion results consist of the most likely model and a set of realizations of the variables of interest. The application of dimensionality reduction methods makes the stochastic inversion more efficient.

Solution of direct and inverse conduction heat transfer problems using the method of fundamental solutions and differential evolution

2020 ◽  
Vol 37 (9) ◽  
pp. 3293-3319
Author(s):  
Adam Basílio ◽  
Fran Sérgio Lobato ◽  
Fábio de Oliveira Arouca
Keyword(s):  
Heat Transfer ◽  
Inverse Problem ◽  
Inverse Problems ◽  
Differential Evolution ◽  
Computational Cost ◽  
Differential Evolution Algorithm ◽  
Fundamental Solutions ◽  
Method Of Fundamental Solutions ◽  
Content Type ◽  
Evolution Algorithm

Purpose The study of heat transfer mechanisms is an area of great interest because of various applications that can be developed. Mathematically, these phenomena are usually represented by partial differential equations associated with initial and boundary conditions. In general, the resolution of these problems requires using numerical techniques through discretization of boundary and internal points of the domain considered, implying a high computational cost. As an alternative to reducing computational costs, various approaches based on meshless (or meshfree) methods have been evaluated in the literature. In this contribution, the purpose of this paper is to formulate and solve direct and inverse problems applied to Laplace’s equation (steady state and bi-dimensional) considering different geometries and regularization techniques. For this purpose, the method of fundamental solutions is associated to Tikhonov regularization or the singular value decomposition method for solving the direct problem and the differential Evolution algorithm is considered as an optimization tool for solving the inverse problem. From the obtained results, it was observed that using a regularization technique is very important for obtaining a reliable solution. Concerning the inverse problem, it was concluded that the results obtained by the proposed methodology were considered satisfactory, as even with different levels of noise, good estimates for design variables in proposed inverse problems were obtained. Design/methodology/approach In this contribution, the method of fundamental solution is used to solve inverse problems considering the Laplace equation. Findings In general, the proposed methodology was able to solve inverse problems considering different geometries. Originality/value The association between the differential evolution algorithm and the method of fundamental solutions is the major contribution.

The inverse problem of recovering the coefficients of a differential equations on a graph

2020 ◽  
Vol 28 (5) ◽  
pp. 727-738
Author(s):  
Victor Sadovnichii ◽  
Yaudat Talgatovich Sultanaev ◽  
Azamat Akhtyamov
Keyword(s):  
Inverse Problem ◽  
Inverse Problems ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Finite Number ◽  
Characteristic Equation ◽  
Arbitrary Number ◽  
New Class ◽  
Finite Set

AbstractWe consider a new class of inverse problems on the recovery of the coefficients of differential equations from a finite set of eigenvalues of a boundary value problem with unseparated boundary conditions. A finite number of eigenvalues is possible only for problems in which the roots of the characteristic equation are multiple. The article describes solutions to such a problem for equations of the second, third, and fourth orders on a graph with three, four, and five edges. The inverse problem with an arbitrary number of edges is solved similarly.

Variational-hemivariational inverse problem for electro-elastic unilateral frictional contact problem

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Othmane Baiz ◽  
Hicham Benaissa ◽  
Zakaria Faiz ◽  
Driss El Moutawakil
Keyword(s):  
Inverse Problem ◽  
Inverse Problems ◽  
Contact Problem ◽  
Existence And Uniqueness ◽  
Frictional Contact ◽  
Hemivariational Inequalities ◽  
Frictional Contact Problem ◽  
Uniqueness Of A Solution

AbstractIn the present paper, we study inverse problems for a class of nonlinear hemivariational inequalities. We prove the existence and uniqueness of a solution to inverse problems. Finally, we introduce an inverse problem for an electro-elastic frictional contact problem to illustrate our results.

Restricted model domain time Radon transforms

Geophysics ◽  
2016 ◽  
Vol 81 (6) ◽  
pp. A17-A21 ◽  
Author(s):  
Juan I. Sabbione ◽  
Mauricio D. Sacchi
Keyword(s):  
Inverse Problem ◽  
Seismic Data ◽  
Computational Cost ◽  
Synthetic Data ◽  
Model Space ◽  
Radon Transforms ◽  
Iterative Solver ◽  
Hard Thresholding ◽  
Restricted Model ◽  
Marine Data

The coefficients that synthesize seismic data via the hyperbolic Radon transform (HRT) are estimated by solving a linear-inverse problem. In the classical HRT, the computational cost of the inverse problem is proportional to the size of the data and the number of Radon coefficients. We have developed a strategy that significantly speeds up the implementation of time-domain HRTs. For this purpose, we have defined a restricted model space of coefficients applying hard thresholding to an initial low-resolution Radon gather. Then, an iterative solver that operated on the restricted model space was used to estimate the group of coefficients that synthesized the data. The method is illustrated with synthetic data and tested with a marine data example.

scholarly journals Effectiveness Testing of an Inverse Method for Balancing Nonlinear Rotordynamic Systems

2018 ◽  
Author(s):  
Sergio G. Torres Cedillo ◽  
Philip Bonello ◽  
Ghaith Ghanim Al-Ghazal ◽  
Jacinto Cortés Pérez ◽  
Alberto Reyes Solis
Keyword(s):  
Inverse Problem ◽  
Inverse Method ◽  
Linear Connection ◽  
The Other ◽  
Squeeze Film ◽  
Squeeze Film Damper ◽  
Operational Conditions ◽  
Non Invasive ◽  
Highly Nonlinear ◽  
Aero Engine

Modern aero-engine structures typically have at least two nested rotors mounted within a flexible casing via squeeze-film damper (SFD) bearings. The inaccessibility of the HP rotor under operational conditions motivates the use of a non-invasive inverse problem procedure for identifying the unbalance. Such an inverse problem requires prior knowledge of the structure and measurements of the vibrations at the casing. Recent work by the authors reported a non-invasive inverse method for the balancing of rotordynamic systems with nonlinear squeeze-film damper (SFD) bearings, which overcomes several limitations of earlier works. However, it was not applied to a common practical configuration wherein the HP rotor is mounted on the casing via just one weak linear connection (retainer spring), with the other connections being highly nonlinear SFDs. The analysis of the present paper considers such a system. It explores the influence of the condition number and how it is affected as the number of sensors and/or measurement speeds is increased. The results show that increasing the number of measurement speeds has a far more significant impact on the conditioning of the problem than increasing the number of sensors. The balancing effectiveness is reasonably good under practical noise level conditions, but significantly lower than obtained for the previously considered simpler configurations.

scholarly journals Wavelet multi-resolution approximation of time-varying frame structure

2018 ◽  
Vol 10 (8) ◽  
pp. 168781401879559 ◽  
Author(s):  
Min Xiang ◽  
Feng Xiong ◽  
Yuanfeng Shi ◽  
Kaoshan Dai ◽  
Zhibin Ding
Keyword(s):  
Parameter Estimation ◽  
Degrees Of Freedom ◽  
Structural Parameters ◽  
Identification Problem ◽  
Frame Structure ◽  
Structural Parameter ◽  
Time Varying ◽  
Engineering Structures ◽  
Time Frequency ◽  
Non Parametric

Engineering structures usually exhibit time-varying behavior when subjected to strong excitation or due to material deterioration. This behavior is one of the key properties affecting the structural performance. Hence, reasonable description and timely tracking of time-varying characteristics of engineering structures are necessary for their safety assessment and life-cycle management. Due to its powerful ability of approximating functions in the time–frequency domain, wavelet multi-resolution approximation has been widely applied in the field of parameter estimation. Considering that the damage levels of beams and columns are usually different, identification of time-varying structural parameters of frame structure under seismic excitation using wavelet multi-resolution approximation is studied in this article. A time-varying dynamical model including both the translational and rotational degrees of freedom is established so as to estimate the stiffness coefficients of beams and columns separately. By decomposing each time-varying structural parameter using one wavelet multi-resolution approximation, the time-varying parametric identification problem is transformed into a time-invariant non-parametric one. In solving the high number of regressors in the non-parametric regression program, the modified orthogonal forward regression algorithm is proposed for significant term selection and parameter estimation. This work is demonstrated through numerical examples which consider both gradual variation and abrupt changes in the structural parameters.

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