Bayesian Parameter Determination of a CT-Test Described by a Viscoplastic-Damage Model Considering the Model Error

The state of materials and accordingly the properties of structures are changing over the period of use, which may influence the reliability and quality of the structure during its life-time. Therefore identification of the model parameters of the system is a topic which has attracted attention in the content of structural health monitoring. The parameters of a constitutive model are usually identified by minimization of the difference between model response and experimental data. However, the measurement errors and differences in the specimens lead to deviations in the determined parameters. In this article, the Choboche model with a damage is used and a stochastic simulation technique is applied to generate artificial data which exhibit the same stochastic behavior as experimental data. Then the model and damage parameters are identified by applying the sequential Gauss-Markov-Kalman filter (SGMKF) approach as this method is determined as the most efficient method for time consuming finite element model updating problems among filtering and random walk approaches. The parameters identified using this Bayesian approach are compared with the true parameters in the simulation, and further, the efficiency of the identification method is discussed. The aim of this study is to observe whether the mentioned method is suitable and efficient to identify the model and damage parameters of a material model, as a highly non-linear model, for a real structural specimen using a limited surface displacement measurement vector gained by Digital Image Correlation (DIC) and to see how much information is indeed needed to estimate the parameters accurately even by considering the model error and whether this approach can also practically be used for health monitoring purposes before the occurrence of severe damage and collapse

[1]  Ehsan Adeli.  Viscoplastic-Damage Model Parameter Identification via Bayesian Methods , 2019 .

[2]  Joel P. Conte,et al.  Nonlinear finite element model updating for damage identification of civil structures using batch Bayesian estimation , 2017 .

[3]  Toshio Nakamura,et al.  Identification of elastic-plastic anisotropic parameters using instrumented indentation and inverse analysis , 2007 .

[4]  Paul Miles,et al.  Bayesian uncertainty analysis of finite deformation viscoelasticity , 2015 .

[5]  Saeed Ziaei-Rad,et al.  Stochastic modelling of clay/epoxy nanocomposites , 2014 .

[6]  T. Hughes,et al.  Space-time finite element methods for elastodynamics: formulations and error estimates , 1988 .

[7]  Tshilidzi Marwala,et al.  Finite Element Model Updating Using Bayesian Framework and Modal Properties , 2005 .

[8]  Wei Zheng,et al.  Bayesian Probabilistic Framework for Damage Identification of Steel Truss Bridges under Joint Uncertainties , 2013 .

[9]  J. Chaboche,et al.  On the Plastic and Viscoplastic Constitutive Equations—Part II: Application of Internal Variable Concepts to the 316 Stainless Steel , 1983 .

[10]  R. Ghanem,et al.  Stochastic Finite Elements: A Spectral Approach , 1990 .

[11]  Giulio Maier,et al.  A constitutive model of metal–ceramic functionally graded material behavior: Formulation and parameter identification , 2008 .

[12]  Thomas Most,et al.  Identification of the parameters of complex constitutive models: Least squares minimization vs. Bayesian updating , 2010 .

[13]  James L. Beck,et al.  Bayesian Learning Using Automatic Relevance Determination Prior with an Application to Earthquake Early Warning , 2008 .

[14]  Elham Mahmoudi,et al.  Reliability-based Robust Design Optimization of a Rock Salt Cavern , 2019 .

[15]  Xiaodong Zhao,et al.  A Bayesian approach for characterization of soft tissue viscoelasticity in acoustic radiation force imaging , 2016, International journal for numerical methods in biomedical engineering.

[16]  T. Rabczuk,et al.  Nonlinear interphase effects on plastic hardening of nylon 6/clay nanocomposites: A computational stochastic analysis , 2020, Journal of Composite Materials.

[17]  Phaedon-Stelios Koutsourelakis,et al.  A multi-resolution, non-parametric, Bayesian framework for identification of spatially-varying model parameters , 2008, J. Comput. Phys..

[18]  K. F. Alvin,et al.  Finite Element Model Update via Bayesian Estimation and Minimization of Dynamic Residuals , 1996 .

[19]  N. Wiener.  The Homogeneous Chaos , 1938 .

[20]  Alberto Corigliano,et al.  Parameter identification of a time-dependent elastic-damage interface model for the simulation of debonding in composites ☆ , 2001 .

[21]  Pietro Croce,et al.  On Bayesian identification methods for the analysis of existing structures , 2016 .

[22]  Ehsan Noroozinejad Farsangi,et al.  Supervised damage and deterioration detection in building structures using an enhanced autoregressive time-series approach , 2020 .

[23]  Raphael T. Haftka,et al.  Introduction to the Bayesian Approach Applied to Elastic Constants Identification , 2010 .

[24]  Khader M. Hamdia,et al.  Uncertainty quantification of the fracture properties of polymeric nanocomposites based on phase field modeling , 2015 .

[25]  Pietro Croce,et al.  Seismic Reliability Assessment of a Concrete Water Tank Based on the Bayesian Updating of the Finite Element Model , 2017 .

[26]  S. Marelli,et al.  Sparse polynomial chaos expansions of frequency response functions using stochastic frequency transformation , 2016, 1606.01662.

[27]  Rolf Mahnken,et al.  Identification of Material Parameters for Constitutive Equations , 2004 .

[28]  Francesco Ubertini,et al.  Estimation of elastic constants of thick laminated plates within a Bayesian framework , 2007 .

[29]  J. McMahon,et al.  Viscoplasticity based on overstress with a differential growth law for the equilibrium stress , 1986 .

[30]  Jan-Eric Ståhl,et al.  Identification of plasticity constants from orthogonal cutting and inverse analysis , 2014 .

[31]  Wael A. Altabey,et al.  Efficiency of grey wolf optimization algorithm for damage detection of skeletal structures via expanded mode shapes , 2020, Advances in Structural Engineering.

[32]  C. S. Manohar,et al.  Bayesian parameter identification in dynamic state space models using modified measurement equations , 2015 .

[33]  Andrew I. Dale,et al.  The theory that would not die , 2012 .

[34]  Nicola Bonora,et al.  Modeling ductile damage under fully reversed cycling , 2003 .

[35]  Oliver Pajonk,et al.  Stochastic Spectral Methods for Linear Bayesian Inference , 2012 .

[36]  A. Vautrin,et al.  Bayesian Identification of Elastic Constants in Multi-Directional Laminate from Moiré Interferometry Displacement Fields , 2012, Experimental Mechanics.

[37]  Sanjay Sampath,et al.  Micro-indentation and inverse analysis to characterize elastic /plastic graded materials , 2003 .

[38]  Kumar Vemaganti,et al.  A Bayesian approach to selecting hyperelastic constitutive models of soft tissue , 2015 .

[39]  Frank Klawonn,et al.  Evaluation of statistical parameters of concrete strength from secondary experimental test data , 2018 .

[40]  Khader M. Hamdia,et al.  Stochastic analysis of the fracture toughness of polymeric nanoparticle composites using polynomial chaos expansions , 2017, International Journal of Fracture.

[41]  Dieter Dinkler,et al.  A nonlocal damage model for mild steel under inelastic cyclic straining , 2012 .

[42]  K. D. Murphy,et al.  Bayesian identification of a cracked plate using a population-based Markov Chain Monte Carlo method , 2011 .

[43]  André Jalobeanu,et al.  Integrating laboratory creep compaction data with numerical fault models: A Bayesian framework , 2007 .

[44]  S. R. Bodner,et al.  A constitutive model for inelastic flow and damage evolution in solids under triaxial compression , 1992 .

[45]  Joel P. Conte,et al.  Extended Kalman filter for material parameter estimation in nonlinear structural finite element models using direct differentiation method , 2015 .

[46]  Pietro Croce,et al.  A BAYESIAN HIERARCHICAL MODEL FOR CLIMATIC LOADS UNDER CLIMATE CHANGE , 2019, Proceedings of the 3rd International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECOMP 2019).

[47]  Alan K. Miller,et al.  An Inelastic Constitutive Model for Monotonic, Cyclic, and Creep Deformation: Part I—Equations Development and Analytical Procedures , 1976 .

[48]  G. Evensen.  Data Assimilation: The Ensemble Kalman Filter , 2006 .

[49]  Hermann G. Matthies,et al.  Bayesian Parameter Estimation via Filtering and Functional Approximations , 2016, 1611.09293.

[50]  Hermann G. Matthies,et al.  Concrete gravity dams model parameters updating using static measurements , 2019, Engineering Structures.

[51]  Jérôme Antoni,et al.  Bayesian characterization of Young's modulus of viscoelastic materials in laminated structures , 2013 .

[52]  M.G. Fujie,et al.  Developing an Intraoperative Methodology Using the Finite Element Method and the Extended Kalman Filter to Identify the Material Parameters of an Organ Model , 2007, 2007 29th Annual International Conference of the IEEE Engineering in Medicine and Biology Society.

[53]  Hermann G. Matthies,et al.  Bayesian parameter identification in plasticity , 2017 .

[54]  Anna De Falco,et al.  Dynamic structural health monitoring for concrete gravity dams based on the Bayesian inference , 2020 .

[55]  O. Wall,et al.  Estimation of Parameters in Viscoplastic and Creep Material Models , 2001, SIAM J. Appl. Math..

[56]  Somayeh Mashayekhi,et al.  Modeling, experimental characterization, and uncertainty quantification of auxetic foams: hyperelastic and fractional viscoelastic mechanics , 2020, Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring.

[57]  E. Noroozinejad Farsangi,et al.  Reliability Assessment and Sensitivity Analysis of Concrete Gravity Dams by Considering Uncertainty in Reservoir Water Levels and Dam Body Materials , 2020 .

[58]  D. Little,et al.  Stochastic Identification of Linear-Viscoelastic Models of Aged and Unaged Asphalt Mixtures , 2015 .

[59]  Hermann G. Matthies,et al.  Parameter Identification in Viscoplasticity using Transitional Markov Chain Monte Carlo Method , 2019, ArXiv.

[60]  Michel Aubertin,et al.  A unified viscoplastic model for the inelastic flow of alkali halides , 1991 .

[61]  Joel P. Conte,et al.  Material Parameter Identification in Distributed Plasticity FE Models of Frame-Type Structures Using Nonlinear Stochastic Filtering , 2015 .

[62]  Harvey Thomas Banks,et al.  Comparison of Frequentist and Bayesian Confidence Analysis Methods on a Viscoelastic Stenosis Model , 2013, SIAM/ASA J. Uncertain. Quantification.

[63]  Nam H. Kim,et al.  Identification of correlated damage parameters under noise and bias using Bayesian inference , 2011 .

[64]  Majid Pouraminian,et al.  Reliability analysis of Pole Kheshti historical arch bridge under service loads using SFEM , 2019, Journal of Building Pathology and Rehabilitation.

[65]  Nicholas Zabaras,et al.  A Bayesian inference approach to the inverse heat conduction problem , 2004 .

[66]  Mohinder S. Grewal,et al.  Kalman Filtering: Theory and Practice Using MATLAB , 2001 .

[67]  J. Chaboche,et al.  On the Plastic and Viscoplastic Constitutive Equations—Part I: Rules Developed With Internal Variable Concept , 1983 .

[68]  Nam H. Kim,et al.  Fatigue life prediction based on Bayesian approach to incorporate field data into probability model , 2011 .

[69]  Hermann G. Matthies,et al.  A deterministic filter for non-Gaussian Bayesian estimation— Applications to dynamical system estimation with noisy measurements , 2012 .

[70]  Pietro Croce,et al.  Probabilistic Seismic Assessment of Existing Masonry Buildings , 2019 .

[71]  Bruno Sudret,et al.  Polynomial chaos expansion for uncertainty quantification of dam engineering problems , 2020 .

[72]  H. Matthies.  Stochastic finite elements: Computational approaches to stochastic partial differential equations , 2008 .

[73]  D. Xiu.  Numerical Methods for Stochastic Computations: A Spectral Method Approach , 2010 .

[74]  Alberto Corigliano,et al.  Simulation of damage in composites by means of interface models: parameter identification , 2001 .

[75]  Tomonari Furukawa,et al.  Stochastic identification of elastic constants for anisotropic materials , 2010 .

[76]  Seyed Sina Kourehli,et al.  Model updating and damage detection in multi-storyshear frames using Salp Swarm Algorithm , 2019 .

[77]  Joel P. Conte,et al.  Bayesian Methods for Nonlinear System Identification of Civil Structures , 2015 .

[78]  Hermann G. Matthies,et al.  Comparison of Bayesian methods on parameter identification for a viscoplastic model with damage , 2020, Probabilistic Engineering Mechanics.

[79]  Man Max Hendriks,et al.  Identification of the mechanical behavior of solid materials , 1991 .

[80]  Juha Töyräs,et al.  Fibril reinforced poroelastic model predicts specifically mechanical behavior of normal, proteoglycan depleted and collagen degraded articular cartilage. , 2003, Journal of biomechanics.

[81]  P. S. Koutsourelakis,et al.  A novel Bayesian strategy for the identification of spatially varying material properties and model validation: an application to static elastography , 2012, 1512.05913.

[82]  Hermann G. Matthies,et al.  Effect of Load Path on Parameter Identification for Plasticity Models using Bayesian Methods , 2019, ArXiv.

[83]  S. Mahadevan,et al.  Bayesian calibration of thermodynamic parameters for geochemical speciation modeling of cementitious materials , 2012 .

[84]  Di Wu,et al.  Interval finite element analysis and reliability-based optimization of coupled structural-acoustic system with uncertain parameters , 2014 .

[85]  G. Maier,et al.  Parameter identification of a cohesive crack model by Kalman filter , 2002 .

[86]  Ehsan Noroozinejad Farsangi,et al.  Probabilistic Safety Evaluation of a Concrete arch dam Based on Finite Element Modeling and A Reliability L-R Approach , 2019 .

[87]  D. Luenberger.  Optimization by Vector Space Methods , 1968 .

[88]  A. Bower.  Applied Mechanics of Solids , 2009 .

[89]  Anna De Falco,et al.  Shedding Light on the Effect of Uncertainties in the Seismic Fragility Analysis of Existing Concrete Dams , 2020, Infrastructures.

[90]  Jean-Claude Golinval,et al.  Structural Damage Diagnosis by Kalman Model Based on Stochastic Subspace Identification , 2004 .

[91]  Mohammad Amin Hariri-Ardebili,et al.  Probabilistic Identification of Seismic Response Mechanism in a Class of Similar Arch Dams , 2019, Infrastructures.