Computational inference of vibratory system with incomplete modal information using parallel, interactive and adaptive Markov chains

Zhou, Kai; Tang, Jiong

doi:10.1016/j.jsv.2021.116331

Cited by 12 publications

(3 citation statements)

References 54 publications

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“…To address this, stochastic linear model updating methods [6][7][8][9], have been developed to determine the physical distribution of the updating parameters that represent variability in measurement data. Over the last decade, there has been a significant number of publications focused on advancing stochastic linear model updating methods, as exemplified by various papers, including [10][11][12][13][14][15][16][17][18]. Stochastic linear model updating aims to improve the accuracy of uncertain parameters in a linear model by fusing experimental measurements with prior knowledge using probability theory [19,20].…”

Section: Stochastic Nonlinear Model Updating In Structural Dynamics U...mentioning

confidence: 99%

Stochastic Nonlinear Model Updating in Structural Dynamics Using a Novel Likelihood Function within the Bayesian-MCMC Framework

Pandey,

Khodaparast,

Friswell

et al. 2024

Preprint

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The study presents a novel approach for stochastic nonlinear model updating in structural dynamics, employing a Bayesian framework integrated with Markov Chain Monte Carlo (MCMC) sampling for parameter estimation by using an approximated likelihood function. The proposed methodology is applied to both numerical and experimental cases. The paper commences by introducing Bayesian inference and its constituents: the likelihood function, prior distribution, and posterior distribution. The resonant decay method is employed to extract backbone curves, which capture the non-linear behavior of the system. A mathematical model based on a single degree of freedom (SDOF) system is formulated, and backbone curves are obtained from time response data. Subsequently, MCMC sampling is employed to estimate the parameters using both numerical and experimental data. The obtained results demonstrate the convergence of the Markov chain, present parameter trace plots, and provide estimates of posterior distributions of updated parameters along with their uncertainties. Experimental validation is performed on a cantilever beam system equipped with permanent magnets and electromagnets. The proposed methodology demonstrates promising results in estimating parameters of stochastic non-linear dynamical systems. Through the use of the proposed likelihood functions using backbone curves, the probability distributions of both linear and non-linear parameters are simultaneously identified. Based on this view, the necessity to segregate stochastic linear and non-linear model updating is eliminated.

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Section: Stochastic Nonlinear Model Updating In Structural Dynamics U...mentioning

confidence: 99%

Stochastic Nonlinear Model Updating in Structural Dynamics Using a Novel Likelihood Function within the Bayesian-MCMC Framework

Pandey,

Khodaparast,

Friswell

et al. 2024

Preprint

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show abstract

“…This paper use MATLAB to deduce the 'Block of Genetic Algorithm' above, and the principle can be described more detailed through Fig. 6 below [10]. In this picture, there is a 'g(F1, F3, F3)' which is consist of Fk, Fk here are three functions above.…”

Section: Genetic Algorithm Based On Dynamic Programming Modelmentioning

confidence: 99%

Research on simulation of control of case application based on optimization model

Yuan

2024

Fourth International Conference on Applied Mathematics, Modelling, and Intelligent Computing (CAMMIC 2024)

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This article introduced a method to optimize the time and energy consumption during riding. First, power curve can be derived to determine the relationship between the rider's position on the course and the force exerted to the rider in different conditions. Then, Markov process can be used to solve the optimization model based on dynamic programming model, and then the optimal strategy is obtained. Afterwards, the sensitivity of the model can be investigated by Functional Analysis. Finally, this paper gave the general process of using genetic algorithm to optimize this model.

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“…Leveraging upon finite element (FE) simulation to map the relation between the damage and resulting impedance/ admittance response change, damage identification can then be facilitated. This approach falls into the general category of FE model updating which has become the mainstream for damage identification analysis (Zhou and Tang, 2016;Sun et al, 2017;Chen et al, 2020;Zhou and Tang, 2021b). In this approach, the damage is represented by the change of the associated structural properties, for example, mass, stiffness, and damping, and can be inversely identified in light of the measurements.…”

Section: Introductionmentioning

confidence: 99%

Probabilistic Multi-Objective Inverse Analysis for Damage Identification Using Piezoelectric Impedance Measurement Under Uncertainties

Zhou

Zhang

et al. 2022

Front. Built Environ.

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Piezoelectric impedance sensing is promising for highly accurate damage identification because of its high-frequency active interrogative nature and simplicity in data acquisition. To fully unleash the potential, effective inverse analysis is needed in order to pinpoint the damage location and identify the severity. The inverse analysis, however, may be underdetermined since there exists a very large number of unknowns (i.e., locations and severity levels) to be solved in a finite element model but only limited measurements are available in actual practice. To uncover the true damage scenario, an inverse analysis strategy built upon the multi-objective optimization, which aims at matching the multiple sets of measurements with model predictions in the damage parametric space, can be formulated to identify a small set of solutions. This solution set then allows the incorporation of empirical knowledge to facilitate final decision-making. The main disadvantage of the conventional inverse analysis strategy is that it overlooks uncertainties that exist in both baseline structural modeling and actual measurements. To address this, in this research, we formulate a probabilistic multi-objective optimization-based inverse analysis framework, which is fundamentally built upon the differential evolution Markov chain Monte Carlo (DEMC) technique. The new approach can yield the Pareto optimal set (solutions) and the respective Pareto front, which are represented in a probabilistic sense to account for uncertainties. Comprehensive case studies with experimental investigations are conducted to demonstrate the effectiveness of this new approach.

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Computational inference of vibratory system with incomplete modal information using parallel, interactive and adaptive Markov chains

Cited by 12 publications

References 54 publications

Stochastic Nonlinear Model Updating in Structural Dynamics Using a Novel Likelihood Function within the Bayesian-MCMC Framework

Stochastic Nonlinear Model Updating in Structural Dynamics Using a Novel Likelihood Function within the Bayesian-MCMC Framework

Research on simulation of control of case application based on optimization model

Probabilistic Multi-Objective Inverse Analysis for Damage Identification Using Piezoelectric Impedance Measurement Under Uncertainties

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