The use of polynomial chaos for parameter identification from measurements in nonlinear dynamical systems

Pandurangan, Rangaraj; Chaudhuri, Abhijit; Gupta, Sayan

doi:10.1002/zamm.201300232

Cited by 4 publications

(3 citation statements)

References 58 publications

(123 reference statements)

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“…Minimization of the computational costs can be achieved if the proposed method is integrated with efficient sampling algorithms, such as, importance sampling or Latin hypercube sampling. Alternative strategies for minimizing the computational costs associated with the bootstrap particle filter by transforming the forward problem into abstract mathematical space have been addressed in a separate study in [49] and are outside the scope of the present work.…”

Section: Discussionmentioning

confidence: 99%

Investigations on a particle filter algorithm for crack identification in beams from vibration measurements

Rangaraj

Pokale

Banerjee

et al. 2015

Struct. Control Health Monit.

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This study focuses on crack identification in beams from vibration measurements using principles of dynamic state estimation. The FEM is used to model the beam with cracked-beam elements that account for the presence of an edge crack under near-tip elasto-plastic conditions. The crack size and its location are treated as the variables that are identified using a particle filter algorithm. A parametric study is first carried out with synthetic measurements to numerically analyze the performance of the algorithm. Subsequently, using measurements acquired from physical experiments involving a cantilever beam subjected to arbitrary excitations, the proposed algorithm is used to identify the size and location of crack-like defects. The proposed method does not require measurements of the undamaged beam, hence, can be used for crack identification in beams for which no earlier measurements are available. antiresonance peaks in the frequency response functions have also been carried out to locate cracks [20][21][22]. Alternative methods that use modal parameters for crack detection include optimization approaches in conjunction with perturbation methods [23] and wavelet analysis [24,25].Time domain-based studies using iterative approaches for locating and estimating the severity of damage from vibration measurements have been discussed in [26][27][28][29][30]. These studies typically introduce the damage into the numerical model either through an unknown variable or a function with unknown parameters. Subsequently, these unknown quantities are estimated through an iterative procedure applied on available response measurements. Unlike modal analysis-based methods, which are primarily applicable to linear systems, these methods are applicable in nonlinear systems [28,29] as well as when measurements are noisy [30,31]. However, inverse methods using deterministic models lack robustness because of the unknown and unavoidable errors that enter the analysis due to the inevitable inaccuracies in mathematical modeling and data acquisition. These errors enter the inverse analysis in the form of noise, which need to be appropriately taken into account.The robustness of inverse methods can be improved by explicit modeling of the uncertainties (i.e., noise) using a probabilistic approach. This has led to adopting Bayesian filtering frameworks in the damage-detection algorithms. The focus in these methods is not on identifying the exact location and sizes of the damage but on defining their corresponding probability density functions (pdf) and estimating their most probable values, conditioned on the available measurements. A set of variables are defined for the system and/or damage parameters to be identified; these are modeled as random variables with an assumed pdf. A vector of realizations for these random variables is simulated in the computer having the specified probabilistic properties. Corresponding to each realization for the system parameters, a mathematical model is used to predict the structure response for a particular...

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Section: Discussionmentioning

confidence: 99%

Investigations on a particle filter algorithm for crack identification in beams from vibration measurements

Rangaraj

Pokale

Banerjee

et al. 2015

Struct. Control Health Monit.

Self Cite

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“…Here, the idea is to replace the computationally expensive physics-based model-the FE modelwith a computationally inexpensive non-physics-based model-the surrogate modelcarrying out the updating of the first through the updating of the second. Applications of the gPCE-based stochastic inverse method for structural identification can be found in [20][21][22][23][24][35][36][37][38][39][40][41][42][43][44].…”

Section: Introductionmentioning

confidence: 99%

gPCE-Based Stochastic Inverse Methods: A Benchmark Study from a Civil Engineer’s Perspective

et al. 2021

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In civil and mechanical engineering, Bayesian inverse methods may serve to calibrate the uncertain input parameters of a structural model given the measurements of the outputs. Through such a Bayesian framework, a probabilistic description of parameters to be calibrated can be obtained; this approach is more informative than a deterministic local minimum point derived from a classical optimization problem. In addition, building a response surface surrogate model could allow one to overcome computational difficulties. Here, the general polynomial chaos expansion (gPCE) theory is adopted with this objective in mind. Owing to the fact that the ability of these methods to identify uncertain inputs depends on several factors linked to the model under investigation, as well as the experiment carried out, the understanding of results is not univocal, often leading to doubtful conclusions. In this paper, the performances and the limitations of three gPCE-based stochastic inverse methods are compared: the Markov Chain Monte Carlo (MCMC), the polynomial chaos expansion-based Kalman Filter (PCE-KF) and a method based on the minimum mean square error (MMSE). Each method is tested on a benchmark comprised of seven models: four analytical abstract models, a one-dimensional static model, a one-dimensional dynamic model and a finite element (FE) model. The benchmark allows the exploration of relevant aspects of problems usually encountered in civil, bridge and infrastructure engineering, highlighting how the degree of non-linearity of the model, the magnitude of the prior uncertainties, the number of random variables characterizing the model, the information content of measurements and the measurement error affect the performance of Bayesian updating. The intention of this paper is to highlight the capabilities and limitations of each method, as well as to promote their critical application to complex case studies in the wider field of smarter and more informed infrastructure systems.

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“…The method in [31] similarly to [30] uses posterior moments from Bayes' rule, but accounts for timevarying additive disturbances and uses the PCE in addition for uncertainty propagation. [32] propose to use PCEs for uncertainty propagation in conjunction with a particle filter.…”

Section: Introductionmentioning

confidence: 99%

Output feedback stochastic nonlinear model predictive control of a polymerization batch process

Bradford

Reble

Imsland

2019

2019 18th European Control Conference (ECC)

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Nonlinear model predictive control (NMPC) is one of the few methods that can handle multivariate nonlinear control problems while accounting for process constraints. Many dynamic models are however affected by significant stochastic uncertainties that can lead to closed-loop performance problems and infeasibility issues. In this paper we propose a novel stochastic NMPC (SNMPC) algorithm to optimize a probabilistic objective while adhering chance constraints for feasibility in which only noisy measurements are observed at each sampling time. The system predictions are assumed to be both affected by parametric and additive stochastic uncertainties. In particular, we use polynomial chaos expansions (PCE) to expand the random variables of the uncertainties. These are updated using a PCE nonlinear state estimator and exploited in the SNMPC formulation. The SNMPC scheme was verified on a complex polymerization semi-batch reactor case study.

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The use of polynomial chaos for parameter identification from measurements in nonlinear dynamical systems

Cited by 4 publications

References 58 publications

Investigations on a particle filter algorithm for crack identification in beams from vibration measurements

Investigations on a particle filter algorithm for crack identification in beams from vibration measurements

gPCE-Based Stochastic Inverse Methods: A Benchmark Study from a Civil Engineer’s Perspective

Output feedback stochastic nonlinear model predictive control of a polymerization batch process

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