A local basis approximation approach for nonlinear parametric model order reduction

The efficient condition assessment of engineered systems requires the coupling of high fidelity models with data extracted from the state of the system `as-is'. In enabling this task, this paper implements a parametric Model Order Reduction (pMOR) scheme for nonlinear structural dynamics, and the particular case of material nonlinearity. A physics-based parametric representation is developed, incorporating dependencies on system properties and/or excitation characteristics. The pMOR formulation relies on use of a Proper Orthogonal Decomposition applied to a series of snapshots of the nonlinear dynamic response. A new approach to manifold interpolation is proposed, with interpolation taking place on the reduced coefficient matrix mapping local bases to a global one. We demonstrate the performance of this approach firstly on the simple example of a shear-frame structure, and secondly on the more complex 3D numerical case study of an earthquake-excited wind turbine tower. Parametric dependence pertains to structural properties, as well as the temporal and spectral characteristics of the applied excitation. The developed parametric Reduced Order Model (pROM) can be exploited for a number of tasks including monitoring and diagnostics, control of vibrating structures, and residual life estimation of critical components.Comment: 23 pages, 28 figure

Parametric reduced order models for output-only vibration-based crack detection in shell structures

ISSN:0888-3270ISSN:1096-121

A Physics-Based Reduction with Monitoring Data Assimilation for Adaptive Representations in Structural Systems

Digital twin representations have become an indispensable tool for delivering data-informed virtualizations of operating systems, especially in structural health monitoring applications. In this context, challenges arise when the response often shifts beyond regular operating conditions due to extreme events such as earthquakes or structural damage. Our work proposes a reduced order modeling for adaptive digital twins, for systems undergoing damage, condition deterioration, or experiencing stochastic excitation. Our approach initiates by featuring a projection-based reduced order model (ROM), relying on proper orthogonal decomposition (POD) and local subspaces to form a low-cost surrogate of the parametrized high-fidelity system that retains a physical connotation. However, extreme events induce loading conditions and model states that challenge the accuracy of such representations. To this end, we propose adopting the derived ROM as a forward simulator and adapt the projection basis on-the-fly during operation via a Gaussian processes regressor (GPR) scheme. During operation, the ROM framework receives response monitoring information from a sparse number of nodes. It employs a suitable condition indicator to highlight the potential low precision of the initial surrogate. Subsequently, the GPR-based scheme utilizes the monitoring input to reconstruct the current deformed configuration of the whole system in an online manner. In turn, this approximation serves as a damaged mode that enriches the projection-based ROM and enables online adaptivity. This coupling yields a ROM equipped with critical features for health monitoring applications such as (near) real-time basis refinement, signaling potentially irreversible consequences, and estimation of the uncertainty in the enrichment mode and the adapted ROM prediction.ISSN:2191-5644ISSN:2191-565

A physics-based, local POD basis approach for multi-parametric reduced order models

At the dawn of Industry 4.0, it has become apparent that assessment of engineered systems should be informed from the state of the system "as-is". To this end, data needs to be fused with adequate and efficient system models. Such system models should account for the underlying physics and the possibly nonlinear dynamic processes involved. This paper introduces a physics-based parametric formulation for nonlinear structural systems. A Reduced Order Model (ROM) of the high fidelity system is developed, retaining the dependencies on system properties and on temporal and spectral characteristics of the excitation. The ROM formulation relies on i) Proper Orthogonal Decomposition applied to snapshots of the nonlinear response, and ii) manifold interpolation of the resulting projection bases. Its performance is evaluated on a 3D earthquake-excited shear frame with nonlinear couplings. The developed ROM can be exploited for a number of tasks including monitoring, diagnostics and residual life estimation of critical components

A local basis approximation approach for nonlinear parametric model order reduction

The efficient condition assessment of engineered systems requires the coupling of high fidelity models with data extracted from the state of the system ‘as-is’. In enabling this task, this paper implements a parametric Model Order Reduction (pMOR) scheme for nonlinear structural dynamics, and the particular case of material nonlinearity. A physics-based parametric representation is developed, incorporating dependencies on system properties and/or excitation characteristics. The pMOR formulation relies on use of a Proper Orthogonal Decomposition applied to a series of snapshots of the nonlinear dynamic response. A new approach to manifold interpolation is proposed, with interpolation taking place on the reduced coefficient matrix mapping local bases to a global one. We demonstrate the performance of this approach firstly on the simple example of a shear-frame structure, and secondly on the more complex 3D numerical case study of an wind turbine tower under a ground motion excitation. Parametric dependence pertains to structural properties, as well as the temporal and spectral characteristics of the applied excitation. The developed parametric Reduced Order Model (pROM) can be exploited for a number of tasks including monitoring and diagnostics, control of vibrating structures, and residual life estimation of critical components.ISSN:0022-460XISSN:1095-856

Earthquake-Induced Damage Estimation in Structural Systems using Parametric Physics-Based Reduced-Order Models

Structural systems are usually characterized by complex dynamic response under earthquake or damage events, which extends beyond the expected behavior during regular operational conditions, posing thus unique and challenging requirements for designing and utilizing digital twins. Such representations have become indispensable due to the ongoing virtualization, and their efficiency in addressing such phenomena is critical, especially in the context of structural health monitoring applications. Our work features parametric Reduced Order Models (ROMs) as efficient, low-order surrogates of parametrized structural, dynamical systems and addresses the challenges of adaptive performance and, subsequently, response prediction under state deterioration or stochastic excitation case studies. Specifically, our approach initiates by deriving a projection-based, reliable ROM, reproducing the high fidelity system dynamics, and capturing any parametric dependencies during an initial system modeling stage. To achieve this, we rely on Proper Orthogonal Decomposition (POD) to approximate the subspace of the response from a set of training evaluations and then project and propagate the respective reduced coordinates’ dynamics. However, extreme loads like those induced by earthquakes challenge the performance limits of such representations during operating conditions as POD restricts the dynamics in a single, linear approximation of the original manifold. In contrast, the actual excitation may lead to substantially different behavior than the instances observed during the training configurations. As a remedy to this issue, we propose adopting the initial ROM as a forward simulator and adapt the projection basis during operation through a Gaussian Processes Regressor (GPR) coupled to the ROM framework. Relying on monitoring output measurements from a sparse number of system channels, a suitable performance indicator signals the failure of the initial surrogate in the event of extreme operating conditions. In turn, the framework enriches the initial projection subspace by employing the GPR-based scheme, which relies upon data assimilation from the monitoring channels to approximate the deformed configuration of the system and assemble the respective ”damaged” mode. This fusion allows for an adaptive ROM as it enables online projection basis refinement during operation, whilst warning for potential irreversible, or even catastrophic, consequences. In addition, the confidence bounds of the refinement mode prediction enable an initial quantification of the uncertainty involved in the output ROM response estimation

A Local Basis Approximation Approach for Nonlinear Parametric Model Order Reduction

The efficient condition assessment of engineered systems requires the coupling of high fidelity models with data extracted from the state of the system `as-is'. In enabling this task, this paper implements a parametric Model Order Reduction (pMOR) scheme for nonlinear structural dynamics, and the particular case of material nonlinearity. A physics-based parametric representation is developed, incorporating dependencies on system properties and/or excitation characteristics. The pMOR formulation relies on use of a Proper Orthogonal Decomposition applied to a series of snapshots of the nonlinear dynamic response. A new approach to manifold interpolation is proposed, with interpolation taking place on the reduced coefficient matrix mapping local bases to a global one. We demonstrate the performance of this approach firstly on the simple example of a shear-frame structure, and secondly on the more complex 3D numerical case study of an earthquake-excited wind turbine tower. Parametric dependence pertains to structural properties, as well as the temporal and spectral characteristics of the applied excitation. The developed parametric Reduced Order Model (pROM) can be exploited for a number of tasks including monitoring and diagnostics, control of vibrating structures, and residual life estimation of critical components

A physics-based, local POD basis approach for multi-parametric reduced order models

At the dawn of Industry 4.0, it has become apparent that assessment of engineered systems should be informed from the state of the system “as-is”. To this end, data needs to be fused with adequate and efficient system models. Such system models should account for the underlying physics and the possibly nonlinear dynamic processes involved. This paper introduces a physics-based parametric formulation for nonlinear structural systems. A Reduced Order Model (ROM) of the high fidelity system is developed, retaining the dependencies on system properties and on temporal and spectral characteristics of the excitation. The ROM formulation relies on i) Proper Orthogonal Decomposition applied to snapshots of the nonlinear response, and ii) manifold interpolation of the resulting projection bases. Its performance is evaluated on a 3D earthquake-excited shear frame with nonlinear couplings. The developed ROM can be exploited for a number of tasks including monitoring, diagnostics and residual life estimation of critical components

Parametric reduced-order modeling for component-oriented treatment and localized nonlinear feature inclusion

We propose coupling a physics-based reduction framework with a suited response decomposition technique to derive a component-oriented reduction (COR) approach, which is suitable for assembly systems featuring localized nonlinearities. Dependencies on influencing parameters are injected into the reduced-order model (ROM), thus ensuring robustness and validity over a domain of parametric inputs, while capturing nonlinear effects. The implemented approach employs individual component modes to capture localized features while additionally relying on reduced modes of a global nature to approximate the system’s dynamics accurately. The global modes are derived from a linear monolithic system, defined as a result of a coordinate separation scheme, which permits the proposed COR-ROM to naturally couple the response between linear and nonlinear subdomains. The derived low-order representation utilizes a proper orthogonal decomposition projection and is additionally reinforced with the inclusion of a hyper-reduction technique to capture the underlying high-fidelity model response while providing accelerated computations. The resulting approach is exemplified in the synthetic case studies of a four-story shear frame with multiple nonlinear regions driven by hysteresis and a large-scale kingpin connection featuring plasticity.ISSN:0924-090XISSN:1573-269