Low-cost simulation using model order reduction in structural health monitoring: Application of balanced proper orthogonal decomposition

Sepehry, Naserodin; Shamshirsaz, Mahnaz; Bakhtiari-Nejad, Firooz

doi:10.1002/stc.1994

Cited by 10 publications

(27 citation statements)

References 20 publications

(45 reference statements)

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“…For thin plates, only two points are used in thickness direction, and for a good accuracy in calculation of stiffness matrix, Gauss quadrature rule has been applied . Three‐dimensional displacements could be defined as follows:

u ((),,, ξ, η, ζ) = \sum_{i} \sum_{j} \sum_{k} h_{i} ((), ξ) h_{j} ((), η) h_{k} ((), ζ) u_{ijk}, v ((),,, ξ, η, ζ) = \sum_{i} \sum_{j} \sum_{k} h_{i} ((), ξ) h_{j} ((), η) h_{k} ((), ζ) v_{ijk}, w ((),,, ξ, η, ζ) = \sum_{i} \sum_{j} \sum_{k} h_{i} ((), ξ) h_{j} ((), η) h_{k} ((), ζ) w_{ijk},

where u ijk , v ijk , and w ijk are nodal displacements; i , j , and k denote the index of nodes in the ξ , η , and ζ directions, respectively. In each element, H matrix, which relates displacement fields to nodal displacements, can be expressed as follows:

bold-italicu = bold-italicHd .

…”

Section: Approachmentioning

confidence: 99%

“…Model order reduction is a powerful tool in control, fluid, and structural dynamics . The objective of model reduction is to develop a model with low number of states without changing the accuracy of the system dynamics.…”

Section: Introductionmentioning

confidence: 99%

“…For determining an appropriate basis, many methods have been suggested. The balanced proper orthogonal decomposition (BPOD) technique has been developed for deriving basis vectors for high‐order systems . The purpose of this method is model order reduction by projecting high‐dimensional data into a lower‐dimensional space.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, a method for generation of time snapshot is proposed on the basis of Rayleigh damping effect. Also, an adaptive method is applied to obtain minimum order of reduced model based on this time snapshot.…”

Section: Introductionmentioning

confidence: 99%

“…Because of very small thickness of plate, in this paper, the 3D spectral element similar to Ha and Chang has been used to model plate‐like structures. Also without any assumption on the 3D model, the GKMC and BPOD as basis vector has been applied to full order model. Finally, experimental results have been used for comparing and verifying GKMC model order reduction.…”

Section: Introductionmentioning

confidence: 99%

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A new model order reduction method based on global kernelk-means clustering: Application in health monitoring of plate using Lamb wave propagation and impedance method

Sepehry

Asadi

Shamshirsaz

et al. 2018

Struct Control Health Monit

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Summary In this paper, a new method based on global kernel k‐means clustering (GKKMC) has been developed as model order reduction to model electromechanical impedance and Lamb wave in a plate structure. First, a model, based on the spectral finite element method, is developed to simulate piezoelectric wafer active sensor (PWAS) induced electromechanical impedance and Lamb wave propagation. Second, the related coupled electromechanical field equations are solved in 3 dimensions, then an electric voltage signal is applied to PWAS actuator, and finally the produced voltage in PWAS sensor is calculated. In reality, high frequency impedance and Lamb wave simulation in a plate need high degrees of freedom, which leads to a very slow simulation in time and frequency domain calculations. To overcome this problem, GKKMC as a model order reduction approach is proposed and applied. For this purpose, in Lamb wave modeling, a time snapshot method based on the Rayleigh damping effect has been introduced. This proposed method not only has a high accuracy and less time to simulate the problem but also needs lower memory than a full order model. A comparison between the results obtained by GKKMC, the conventional balanced proper orthogonal decomposition method, and a full order method with experimental results have been carried out demonstrating a good agreement. The results show that using this new model order reduction based on GKKMC, simulation time speedups can be reached up to 6 times faster compared with applying a conventional balanced proper orthogonal decomposition method.

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u ((),,, ξ, η, ζ) = \sum_{i} \sum_{j} \sum_{k} h_{i} ((), ξ) h_{j} ((), η) h_{k} ((), ζ) u_{ijk}, v ((),,, ξ, η, ζ) = \sum_{i} \sum_{j} \sum_{k} h_{i} ((), ξ) h_{j} ((), η) h_{k} ((), ζ) v_{ijk}, w ((),,, ξ, η, ζ) = \sum_{i} \sum_{j} \sum_{k} h_{i} ((), ξ) h_{j} ((), η) h_{k} ((), ζ) w_{ijk},

bold-italicu = bold-italicHd .

…”

Section: Approachmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A new model order reduction method based on global kernelk-means clustering: Application in health monitoring of plate using Lamb wave propagation and impedance method

Sepehry

Asadi

Shamshirsaz

et al. 2018

Struct Control Health Monit

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Fatigue Damage Identification and Remaining Useful Life Estimation of Composite Structures Using Piezo Wafer Active Transducers

Loendersloot¹,

Ehsani

Shamshirsaz

2020

Advances in Asset Management and Condition Monitoring

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The prediction of fatigue damage accumulation is a crucial element in the estimation of the Remaining Useful Life of composite structures subjected to cyclic loading. In this paper, two Glass-Fibre Reinforced Plastics, a thin strip and a thick beam, are subjected to fatigue load while being monitored with Piezo Wafer Active Sensors. Two distinct methods, one based on Electro-Mechanical Impedance Spectroscopy (EMIS) and one based on the Reconstruction Algorithm for Probabilistic Identification of Damage (RAPID), are employed. Both methods are mostly used for damage detection, yet not for damage accumulation monitoring. The results presented in this paper show that damage accumulation can be followed during fatigue loading of the test objects. The trends shown in the damage accumulation graphs give an indication of the damage accumulation, and even a change in the damage evolution stage, yet a complete RUL estimation is not possible without further analysis of the experiments, possibly assisted by numerical modelling.

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Numerical Modelling of Stochastic Fatigue Damage Accumulation in Thick Composites

Loendersloot

Ehsani

Sepehry

et al. 2021

Lecture Notes in Civil Engineering

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In an earlier research, experimental evidence was given on the ability to use Piezo Wafer Active Sensors and acousto-ultrasonics to monitor the accumulation of fatigue damage in a thick composite structure. As a next step, numerical models are investigated as they aid in the further understanding of the governing phenomena and a quantification of the accumulated damage. However, they suffer from high computational demands, due to a high mesh density, the stochastic nature of crack initiation and the combination of initiation and propagation of cracks.The Polynomial Chaos Expansion (PCE) method is employed to efficiently make meta models and, with these models, account for the stochastic behaviour of crack initiation and formation of delaminations. The meta models thus allow predicting the overall effect of damage accumulations within certain bounds of uncertainty. This aids in the quantification of damage accumulation, hence allowing for a damage severity estimation based on the experimental results.The input for the PCE method is a 2D Finite Element (FE) model. Cracks and delaminations are generated using Random Variables (RV) describing the geometrical position and length and orientation. Moreover, the number of cracks and delaminations is randomized as well. The necessary remeshing is done automatically, allowing for a completely automated simulation for a large number of FE simulations to feed the PCE model.Several Quantities of Interests (QoI) are defined and tested against their sensitivity to the increasing amount of damage accumulation. A global sensitivity analysis is used to identify the importance of each of the Random Variables. Random variables with a low sensitivity can be eliminated from the analysis, improving the efficiency.

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Low-cost simulation using model order reduction in structural health monitoring: Application of balanced proper orthogonal decomposition

Cited by 10 publications

References 20 publications

A new model order reduction method based on global kernelk-means clustering: Application in health monitoring of plate using Lamb wave propagation and impedance method

A new model order reduction method based on global kernelk-means clustering: Application in health monitoring of plate using Lamb wave propagation and impedance method

Fatigue Damage Identification and Remaining Useful Life Estimation of Composite Structures Using Piezo Wafer Active Transducers

Numerical Modelling of Stochastic Fatigue Damage Accumulation in Thick Composites

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