scholarly journals Parametric Model Order Reduction of Guided Ultrasonic Wave Propagation in Fiber Metal Laminates with Damage

Modelling ◽  
2021 ◽  
Vol 2 (4) ◽  
pp. 591-608
Author(s):  
Nanda Kishore Bellam Muralidhar ◽  
Natalie Rauter ◽  
Andrey Mikhaylenko ◽  
Rolf Lammering ◽  
Dirk A. Lorenz
Keyword(s):  
Wave Propagation ◽  
Ultrasonic Wave ◽  
Model Order Reduction ◽  
Order Reduction ◽  
Parametric Model ◽  
Model Order ◽  
Reduced Order ◽  
Ultrasonic Wave Propagation ◽  
Parametric Model Order Reduction ◽  
Fiber Metal

This paper focuses on parametric model order reduction (PMOR) of guided ultrasonic wave propagation and its interaction with damage in a fiber metal laminate (FML). Structural health monitoring in FML seeks to detect, localize and characterize the damage with high accuracy and minimal use of sensors. This can be achieved by the inverse problem analysis approach, which employs the signal measurement data recorded by the embedded sensors in the structure. The inverse analysis requires us to solve the forward simulation of the underlying system several thousand times. These simulations are often exorbitantly expensive and trigger the need for improving their computational efficiency. A PMOR approach hinged on the proper orthogonal decomposition method is presented in this paper. An adaptive parameter sampling technique is established with the aid of a surrogate model to efficiently update the reduced-order basis in a greedy fashion. A numerical experiment is conducted to illustrate the parametric training of the reduced-order model. The results show that the reduced-order solution based on the PMOR approach is accurately complying with that of the high fidelity solution.

scholarly journals Parametric Model Order Reduction of Guided Ultrasonic Wave Propagation in Fiber Metal Laminates with Damage

2021 ◽  
Author(s):  
Nanda Kishore Bellam Muralidhar ◽  
Natalie Rauter ◽  
Andrey Mikhaylenko ◽  
Rolf Lammering ◽  
Dirk A. Lorenz
Keyword(s):  
Wave Propagation ◽  
Ultrasonic Wave ◽  
Model Order Reduction ◽  
Order Reduction ◽  
Parametric Model ◽  
Model Order ◽  
Reduced Order ◽  
Ultrasonic Wave Propagation ◽  
Parametric Model Order Reduction ◽  
Fiber Metal

This paper focuses on parametric model order reduction (PMOR) of guided ultrasonic wave propagation and its interaction with damage in a fiber metal laminate (FML). Structural health monitoring in FML seeks to detect, localize and characterize the damage with high accuracy and minimal use of sensors. This can be achieved by the inverse problem analysis approach which employs the signal measurement data recorded by the embedded sensors in the structure. The inverse analysis requires to solve the forward simulation of the underlying system several thousand times. These simulations are often exorbitantly expensive and triggered the need for improving their computational efficiency. A PMOR approach hinged on the proper orthogonal decomposition method is presented in this paper. An adaptive parameter sampling technique is established with the aid of a surrogate model to efficiently update the reduced-order basis in a greedy fashion. A numerical experiment is conducted to illustrate the parametric training of the reduced-order model. The results show that the reduced-order solution based on the PMOR approach is accurately complying with that of the high fidelity solution.

scholarly journals Two-Step Predict and Correct Non-Intrusive Parametric Model Order Reduction for Changing Well Locations Using a Machine Learning Framework

Energies ◽  
2021 ◽  
Vol 14 (6) ◽  
pp. 1765
Author(s):  
Hardikkumar Zalavadia ◽  
Eduardo Gildin
Keyword(s):  
Machine Learning ◽  
Error Correction ◽  
Model Order Reduction ◽  
Order Reduction ◽  
Error Correction Model ◽  
Parametric Model ◽  
Model Order ◽  
Correction Model ◽  
Reduced Order ◽  
Parametric Model Order Reduction

The objective of this paper is to develop a two-step predict and correct non-intrusive Parametric Model Order Reduction (PMOR) methodology for the problem of changing well locations in an oil field that can eventually be used for well placement optimization to gain significant computational savings. In this work, we propose a two-step PMOR procedure, where, in the first step, a Proper Orthogonal Decomposition (POD)-based strategy that is non-intrusive to the simulator source code is introduced, as opposed to the convention of using POD as a simulator intrusive procedure. The non-intrusiveness of the proposed technique stems from formulating a novel Machine Learning (ML)-based framework used with POD. The features of the ML model (Random Forest was used here) are designed such that they take into consideration the temporal evolution of the state solutions and thereby avoid simulator access for the time dependency of the solutions. The proposed PMOR method is global, since a single reduced-order model can be used for all the well locations of interest in the reservoir. We address the major challenge of the explicit representation of the well location change as a parameter by introducing geometry-based features and flow diagnostics-inspired physics-based features. In the second step, an error correction model based on reduced model solutions is formulated to correct for discrepancies in the state solutions at well grid blocks expected from POD basis for new well locations. The error correction model proposed uses Artificial Neural Networks (ANNs) that consider the physics-based reduced model solutions as features, and is proved to reduce the error in QoI (Quantities of Interest), such as oil production rates and water cut, significantly. This workflow is applied to a simple homogeneous reservoir and a heterogeneous channelized reservoir using a section of SPE10 model that showed promising results in terms of model accuracy. Speed-ups of about 50×–100× were observed for different cases considered when running the test scenarios. The proposed workflow for Reduced-Order Modeling is “non-intrusive” and hence can increase its applicability to any simulator used. Additionally, the method is formulated such that all the simulation time steps are independent and hence can make use of parallel resources very efficiently and also avoid stability issues that can result from error accumulation over time steps.

scholarly journals An adaptive sampling procedure for parametric model order reduction by matrix interpolation

2019 ◽  
Vol 39 (4) ◽  
pp. 821-834
Author(s):  
Ying Liu ◽  
Hongguang Li ◽  
Huanyu Du ◽  
Ningke Tong ◽  
Guang Meng
Keyword(s):  
Adaptive Sampling ◽  
Model Order Reduction ◽  
Order Reduction ◽  
Parametric Model ◽  
Sampling Procedure ◽  
Model Order ◽  
Reduced Order ◽  
Parametric Model Order Reduction ◽  
Error Indicator ◽  
Matrix Interpolation

An adaptive sampling approach for parametric model order reduction by matrix interpolation is developed. This approach is based on an efficient exploration of the candidate parameter sets and identification of the points with maximum errors. An error indicator is defined and used for fast evaluation of the parameter points in the configuration space. Furthermore, the exact error of the model with maximum error indicator is calculated to determine whether the adaptive sampling procedure reaches a desired error tolerance. To improve the accuracy, the orthogonal eigenvectors are utilized as the reduced-order basis. The proposed adaptive sampling procedure is then illustrated by application in the moving coil of electrical-dynamic shaker. It is shown that the new method can sample the parameter space adaptively and efficiently with the assurance of the resulting reduced-order models’ accuracy.

scholarly journals A Local Basis Approximation Approach for Nonlinear Parametric Model Order Reduction Paper Draft

2021 ◽  
pp. 116055
Author(s):  
Konstantinos Vlachas ◽  
Konstantinos Tatsis ◽  
Konstantinos Agathos ◽  
Adam R. Brink ◽  
Eleni Chatzi
Keyword(s):  
Model Order Reduction ◽  
Order Reduction ◽  
Parametric Model ◽  
Model Order ◽  
Approximation Approach ◽  
Parametric Model Order Reduction ◽  
Local Basis
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