Efficient Reduced-Order Modeling and Response Approximation for Cracked Structures

2017 ◽  
Author(s):  
Meng-Hsuan Tien ◽  
Tianyi Hu ◽  
Kiran D’Souza
Keyword(s):  
Piecewise Linear ◽  
Computational Effort ◽  
Combined Method ◽  
Mass System ◽  
Reduced Order ◽  
Relative Coordinates ◽  
Model Size ◽  
Cracked Structures ◽  
Failure Prognosis ◽  
Three Degree Of Freedom

Analysis of the influence of cracks on the dynamics of structures is critical for design, failure prognosis, and structural health monitoring. Predicting the dynamics of complex cracked structures is computationally challenging for two reasons: (1) the model size is generally large, and (2) the piecewise-linear nonlinearity caused by contact eliminates the use of linear analysis tools. Recently, a technique referred to as X-Xr approach was developed to efficiently reduce the model size of cracked structures. The method employs relative coordinates to describe the motion of crack surfaces such that an effective model reduction can be achieved using Craig-Bampton component mode synthesis. More recently, a method referred to as the generalized bilinear amplitude approximation (generalized BAA) was developed to approximate the amplitude and frequency of piecewise-linear nonlinear systems. This paper modifies the generalized BAA method and combines it with the X-Xr approach to efficiently predict the dynamics of complex cracked structures. The combined method is able to estimate the amplitude and frequency of cracked systems with a reduced computational effort. The proposed approach is demonstrated on a three degree of freedom spring-mass system and a cracked cantilever beam.

Generalized Bilinear Amplitude Approximation and X-Xr for Modeling Cyclically Symmetric Structures With Cracks

2018 ◽  
Vol 140 (4) ◽  
Author(s):  
Meng-Hsuan Tien ◽  
Tianyi Hu ◽  
Kiran D'Souza
Keyword(s):  
Degrees Of Freedom ◽  
Piecewise Linear ◽  
Computational Effort ◽  
Bladed Disks ◽  
Mass System ◽  
Bladed Disk ◽  
Relative Coordinates ◽  
Model Size ◽  
Failure Prognosis ◽  
Symmetric Structures

The analysis of the influence of cracks on the dynamics of bladed disks is critical for design, failure prognosis, and structural health monitoring. Predicting the dynamics of cracked bladed disks is computationally challenging for two reasons: (1) the model size is quite large and (2) the piecewise-linear nonlinearity caused by contact eliminates the use of linear analysis tools. Recently, a technique referred to as the X-Xr approach was developed to efficiently reduce the model size of the cracked bladed disks. The method employs relative coordinates to describe the motion of crack surfaces such that an effective model reduction can be achieved using single sector calculations. More recently, a method referred to as the generalized bilinear amplitude approximation (BAA) was developed to approximate the amplitude and frequency of piecewise-linear nonlinear systems. This paper modifies the generalized BAA method and combines it with the X-Xr approach to efficiently predict the dynamics of the cracked bladed disks. The combined method is able to construct the reduced-order model (ROM) of full disks using single-sector models only and estimate the amplitude and frequency with a significantly reduced computational effort. The proposed approach is demonstrated on a three degrees-of-freedom (DOF) spring–mass system and a cracked bladed disk.

Subspace Trajectory Piecewise-Linear Model Order Reduction for Nonlinear Circuits

2013 ◽  
Vol 14 (3) ◽  
pp. 639-663 ◽  
Author(s):  
Xiaoda Pan ◽  
Hengliang Zhu ◽  
Fan Yang ◽  
Xuan Zeng
Keyword(s):  
State Space ◽  
Model Order Reduction ◽  
Large Scale ◽  
Piecewise Linear ◽  
Order Reduction ◽  
Nonlinear Circuits ◽  
Model Order ◽  
Reduced Order ◽  
Dimensional State Space ◽  
Model Size

AbstractDespite the efficiency of trajectory piecewise-linear (TPWL) model order reduction (MOR) for nonlinear circuits, it needs large amount of expansion points for large-scale nonlinear circuits. This will inevitably increase the model size as well as the simulation time of the resulting reduced macromodels. In this paper, subspace TPWL-MOR approach is developed for the model order reduction of nonlinear circuits. By breaking the high-dimensional state space into several subspaces with much lower dimensions, the subspace TPWL-MOR has very promising advantages of reducing the number of expansion points as well as increasing the effective region of the reduced-order model in the state space. As a result, the model size and the accuracy of the TWPL model can be greatly improved. The numerical results have shown dramatic reduction in the model size as well as the improvement in accuracy by using the subspace TPWL-MOR compared with the conventional TPWL-MOR approach.

scholarly journals Fast Motion Model of Road Vehicles with Artificial Neural Networks

Electronics ◽  
2021 ◽  
Vol 10 (8) ◽  
pp. 928
Author(s):  
Ferenc Hegedüs ◽  
Péter Gáspár ◽  
Tamás Bécsi
Keyword(s):  
Neural Networks ◽  
Artificial Neural Networks ◽  
Dynamic Model ◽  
Piecewise Linear ◽  
Complex Problem ◽  
Computational Effort ◽  
Road Vehicles ◽  
Vehicle Motion ◽  
Artificial Neural ◽  
Original Dynamic

Nonlinear optimization-based motion planning algorithms have been successfully used for dynamically feasible trajectory planning of road vehicles. However, the main drawback of these methods is their significant computational effort and thus high runtime, which makes real-time application a complex problem. Addressing this field, this paper proposes an algorithm for fast simulation of road vehicle motion based on artificial neural networks that can be used in optimization-based trajectory planners. The neural networks are trained with supervised learning techniques to predict the future state of the vehicle based on its current state and driving inputs. Learning data is provided for a wide variety of randomly generated driving scenarios by simulation of a dynamic vehicle model. The realistic random driving maneuvers are created on the basis of piecewise linear travel velocity and road curvature profiles that are used for the planning of public roads. The trained neural networks are then used in a feedback loop with several variables being calculated by additional numerical integration to provide all the outputs of the original dynamic model. The presented model can be capable of short-term vehicle motion simulation with sufficient precision while having a considerably faster runtime than the original dynamic model.

Reduced-Order Time-Domain Simulation of Floating Bodies for Efficient Design Analysis

2015 ◽  
Author(s):  
Hyun Y. Kim ◽  
Stephanie L. Fitzpatrick ◽  
David C. Kring
Keyword(s):  
Memory Function ◽  
Computational Effort ◽  
Impulse Response Functions ◽  
Time Domain Simulation ◽  
Efficient Design ◽  
Floating Bodies ◽  
Order Model ◽  
Reduced Order ◽  
Multi Body ◽  
Multiple Floating Bodies

This paper describes the development and implementation of a reduced-order model to represent the hydrodynamic forces acting on a ship using Impulse-Response Functions (IRF). The approach will be conducted using Aegir, a timedomain seakeeping program that uses an advanced, Non-Rational Uniform B-Spline (NURBS) based, high-order boundary element method. The Cummins equation is slightly modified such that the memory function is decomposed into two terms: one for the impulsive velocity and the other term for the impulsive displacement. The present approach also further develops a method to simulate interactions between multiple floating bodies. The IRF convolutions for the free surface memory effect significantly reduce the computational effort compared to direct simulation. This will be demonstrated for both single and multi-body forward-speed, seakeeping simulations.

Energy harvesting from aeroelastic vibrations induced by discrete gust loads

2016 ◽  
Vol 28 (1) ◽  
pp. 47-62 ◽  
Author(s):  
Claudia Bruni ◽  
James Gibert ◽  
Giacomo Frulla ◽  
Enrico Cestino ◽  
Pier Marzocca
Keyword(s):  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Flow Region ◽  
Rotational Displacement ◽  
Reduced Order ◽  
Piezoelectric Elements ◽  
Out Of Plane ◽  
Gust Loads ◽  
Three Degree Of Freedom ◽  
Euler Bernoulli Beam

This article evaluates the amount of energy that can be extracted from a gust using an aeroelastic energy harvester composed of a flexible wing with attached piezoelectric elements. The harvester operates in a subcritical flow region. It is modeled as a linear Euler–Bernoulli beam sandwiched between two piezoceramics. The extended Hamilton’s principle is used to derive the harvester’s equations of motion and an eigenfunction expansion is used to form a three-degree-of-freedom reduced-order model. The degrees of freedom retained in the model are two flexural degrees for the in-plane and out-of-plane displacements, and a torsional degree for the rotational displacement. Wagner and Küssner functions are used to represent the unsteady aerodynamic and gust loading, respectively. The amount of energy extracted from the system is then compared for two different deterministic gust profiles, 1-COSINE and two sharp-edged gusts forming a square gust, for various magnitudes and durations. The results show that the harvester is able to extract more energy from the square gust profile, although for both profiles the harvester extracts more power after the gust has subsided.

From the Digital-Twin to the Cyber Physical System Using Integrated Multidisciplinary Simulation

2021 ◽  
pp. 18-39
Author(s):  
Daniele Catelani
Keyword(s):  
Virtual Worlds ◽  
Computational Effort ◽  
Model Complexity ◽  
Reduced Order ◽  
Digital Twin ◽  
Order Of Magnitude ◽  
Design Production ◽  
Multidisciplinary Simulation ◽  
Lifecycle Management ◽  
Production And Operation

Simulation has been a competitive differentiator for engineering-driven businesses, available at all stages of the development process and lifecycle, used by the various domains within an organization, not necessarily simulation experts. It requires discipline integration, scalability, reduced-order model, and democratization. The concept of digital transformation involves new approaches for data and lifecycle management, the understanding of the digital thread, digital twin, predictive and cognitive capabilities, including improvement of model complexity, integration of physics, increase of knowledge. These trends require bringing the physical and virtual worlds closer together and also the adoption of cyber-physical model at all stages of design, production, and operation. To overcome the drawback of simulation and the need to balance the computational effort with accuracy and efficiency, new modelization strategies are adopted with ML and AI, which use a combination of virtual and physical data for training ROM, with an order of magnitude faster than the multiphysics one.

Fast Solution of Transient Elastohydrodynamic Line Contact Problems Using the Trajectory Piecewise Linear Approach

2015 ◽  
Vol 138 (1) ◽  
Author(s):  
Daniel Maier ◽  
Corinna Hager ◽  
Hartmut Hetzler ◽  
Nicolas Fillot ◽  
Philippe Vergne ◽  
...  
Keyword(s):  
Piecewise Linear ◽  
Contact Problems ◽  
Galerkin Projection ◽  
Line Contact ◽  
Reduced Order ◽  
Fast Solution ◽  
Speed Up ◽  
Newton Raphson ◽  
First Time ◽  
Piecewise Linear Approach

In order to obtain a fast solution scheme, the trajectory piecewise linear (TPWL) method is applied to the transient elastohydrodynamic (EHD) line contact problem for the first time. TPWL approximates the nonlinearity of a dynamical system by a weighted superposition of reduced linearized systems along specified trajectories. The method is compared to another reduced order model (ROM), based on Galerkin projection, Newton–Raphson scheme and an approximation of the nonlinear reduced system functions. The TPWL model provides further speed-up compared to the Newton–Raphson based method at a high accuracy.

Component-Mode-Based Reduced Order Modeling Techniques for Mistuned Bladed Disks—Part I: Theoretical Models

2000 ◽  
Vol 123 (1) ◽  
pp. 89-99 ◽  
Author(s):  
R. Bladh ◽  
M. P. Castanier ◽  
C. Pierre
Keyword(s):  
Modal Analysis ◽  
Theoretical Models ◽  
Complex Structures ◽  
Bladed Disks ◽  
Component Structure ◽  
Reduced Order ◽  
Practical Applications ◽  
Dynamic Analyses ◽  
Modeling Techniques ◽  
Model Size

Component mode synthesis (CMS) techniques are widely used for dynamic analyses of complex structures. Significant computational savings can be achieved by using CMS, since a modal analysis is performed on each component structure (substructure). Mistuned bladed disks are a class of structures for which CMS is well suited. In the context of blade mistuning, it is convenient to view the blades as individual components, while the entire disk may be treated as a single component. Individual blade mistuning may then be incorporated into the CMS model in a straightforward manner. In this paper, the Craig–Bampton (CB) method of CMS is formulated specifically for mistuned bladed disks, using a cyclic disk description. Then a novel secondary modal analysis reduction technique (SMART) is presented: a secondary modal analysis is performed on a CB model, yielding significant further reduction in model size. In addition, a straightforward non-CMS method is developed in which the blade mistuning is projected onto the tuned system modes. Though similar approaches have been reported previously, here it is generalized to a form that is more useful in practical applications. The theoretical models are discussed and compared from both computational and practical perspectives. It is concluded that using SMART, based on a CB model, has tremendous potential for highly efficient, accurate modeling of the vibration of mistuned bladed disks.

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