Uniqueness of Solutions for the Identification of Linear Reduced Order Structural Systems

2004 ◽  
Author(s):  
Guillermo Franco ◽  
Jun Yu ◽  
Raimondo Betti
Keyword(s):  
Degrees Of Freedom ◽  
Optimization Technique ◽  
Identification Problem ◽  
Structural Systems ◽  
Uniqueness Of Solutions ◽  
Reduced Order ◽  
Theoretical Approaches ◽  
Uniqueness Of The Solution ◽  
Minimum Number ◽  
Output Information

The problem of identification of structural systems is an inverse problem that uses input (say force excitation) and output information (accelerations, for instance) to obtain an optimal model to describe the system’s behavior. Since a full instrumentation setup is expensive, situations usually arise where only partial measurements are available. Uniqueness of the solution in these circumstances might not be guaranteed. This paper analyzes the minimum number of measurements required to ensure that only one solution exists for the identification problem of mass, damping and stiffness distributions of shear-type N degrees of freedom linear structures. Three typical configurations of measurements are studied with two distinct theoretical approaches, one based on classical polynomial theory, the other based on reduced order model theory. Both these approaches lead to the conclusion that only one input and one or two output measurements are sufficient to guarantee uniqueness of identification, depending on the selected location of the input measurement. Additionally, the identification of a 3DOF system is carried out analytically with the usage of Sylvester’s Dyalitic Elimination to show that fewer measurements than the ones proposed lead to non-unique identification. This fact is also illustrated with the usage of a recently developed optimization technique, with which convergence to the different solutions is observed depending on the initial estimate used.

On the Uniqueness of Solutions for the Identification of Linear Structural Systems

2005 ◽  
Vol 73 (1) ◽  
pp. 153-162 ◽  
Author(s):  
Guillermo Franco ◽  
Raimondo Betti ◽  
Richard W. Longman
Keyword(s):  
Prior Knowledge ◽  
Degrees Of Freedom ◽  
Identification Problem ◽  
Minimum Amount ◽  
Structural Systems ◽  
Structural System ◽  
Uniqueness Of Solutions ◽  
Stiffness Identification ◽  
Shear Type ◽  
Forced Excitation

This work tackles the problem of global identifiability of an undamped, shear-type, N degrees of freedom linear structural system under forced excitation without any prior knowledge of its mass or stiffness distributions. Three actuator/sensor schemes are presented, which guarantee the existence of only one solution for the mass and stiffness identification problem while requiring a minimum amount of instrumentation (only 1 actuator and 1 or 2 sensors). Through a counterexample for a 3DOF system it is also shown that fewer measurements than those suggested result invariably in non-unique solutions.

Distributed Friction and Microslip in Mechanical Joints With Varying Degrees-of-Freedom

2001 ◽  
Author(s):  
D. Dane Quinn
Keyword(s):  
Degrees Of Freedom ◽  
Degree Of Freedom ◽  
External Forcing ◽  
Reduced Order ◽  
Mechanical Joints ◽  
Starting Point ◽  
Minimum Number ◽  
Frictional Forces ◽  
Distributed Friction ◽  
Structural Interfaces

Abstract This work considers the effect of distributed friction on the dynamics arising from a simple model for a jointed structure. A hierarchy of models is developed, parameterized by the degree-of-freedom n, which physically corresponds to the number of possible slip zones. When the resulting system is subjected to harmonic forcing, numerical simulations indicate that the instantaneous power dissipated by the frictional forces is sensitive to n. However, the frictional work per unit forcing cycle is, surprisingly, relatively insensitive to the degree-of-freedom, provided n is greater that some minimum number which depends on the amplitude of the external forcing as well as the maximum frictional force. Finally, representative simulations are shown as both the amplitude and frequency of the external forcing are varied. This model provides a starting point for the development of reduced-order models of structural interfaces.

Dynamic Condensation and Synthesis of Unsymmetric Structural Systems

2002 ◽  
Vol 69 (5) ◽  
pp. 610-616 ◽  
Author(s):  
G. Visweswara Rao
Keyword(s):  
Model Reduction ◽  
Degrees Of Freedom ◽  
Structural Systems ◽  
Structural System ◽  
Lanczos Algorithm ◽  
Order Model ◽  
Reduction Procedure ◽  
Reduced Order ◽  
Large Size ◽  
Dynamic Condensation

In this paper model reduction of an unsymmetric and damped structural system is presented using a two-sided dynamic condensation technique. The method is an iterative one and essentially utilizes orthonormalized complex eigenvectors of the unsymmetric system. The eigensolution of the reduced order model with specified master degrees-of-freedom is obtained by Lanczos algorithm. The model reduction procedure is further utilized in substructure synthesis and eigenvalue analysis of large size unsymmetric systems. Application of the condensation technique is illustrated via two example problems of rotor bearing systems.

Stiffness Matrix Properties for Reduced Order Models of Linear Structural Systems

2010 ◽  
Vol 77 (6) ◽  
Author(s):  
Jun Yu ◽  
Maura Imbimbo ◽  
Raimondo Betti
Keyword(s):  
Theoretical Approach ◽  
Stiffness Matrix ◽  
Degrees Of Freedom ◽  
Numerical Procedure ◽  
Structural Systems ◽  
Reduced Order Models ◽  
Reduced Order ◽  
Dependency Relationship ◽  
Matrix Properties

This paper discusses a theoretical approach to investigate the dependency relationship between the stiffness matrix and the complex eigenvectors in the identification of structural systems for the case of insufficient instrumentation setup. The main result of the study consists of proving, in the case of classical damping, the independency of the stiffness subpartition corresponding to the measured degrees-of-freedom from the unmeasured ones. The same result is shown to be valid in the case of nonclassical damping but only for tridiagonal sparse stiffness matrix systems. A numerical procedure proves the above results and also shows the dependency relationship for the general nonclassical damping cases.

scholarly journals Identification of time-varying systems with partial acceleration measurements by synthesis of wavelet decomposition and Kalman filter

2020 ◽  
Vol 12 (6) ◽  
pp. 168781402093046
Author(s):  
Siyi Chen ◽  
Jubin Lu ◽  
Ying Lei
Keyword(s):  
Kalman Filter ◽  
Degrees Of Freedom ◽  
Structural Parameters ◽  
Parametric Identification ◽  
Identification Problem ◽  
Structural Systems ◽  
Wavelet Expansion ◽  
Time Varying ◽  
Multiresolution Decomposition ◽  
Original Time

Structural systems often exhibit time-varying dynamic characteristics during their service life due to serve hazards and environmental erosion, so the identification of time-varying structural systems is an important research topic. Among the previous methodologies, wavelet multiresolution analysis for time-varying structural systems has gained increasing attention in the past decades. However, most of the existing wavelet-based identification approaches request the full measurements of structural responses including acceleration, velocity, and displacement responses at all dynamic degrees of freedom. In this article, an improved algorithm is proposed for the identification of time-varying structural parameters using only partial measurements of structural acceleration responses. The proposed algorithm is based on the synthesis of wavelet multiresolution decomposition and the Kalman filter approach. The time-varying structural stiffness and damping parameters are expanded at multi-scale profile by wavelet multiresolution decomposition, so the time-varying parametric identification problem is converted into a time-invariant one. Structural full responses are estimated by Kalman filter using partial observations of structural acceleration responses. The scale coefficients by the wavelet expansion are estimated via the solution of a nonlinear optimization problem of minimizing the errors between estimated and observed accelerations. Finally, the original time-varying parameters can be reconstructed. To demonstrate the efficiency of the proposed algorithm, the identification of several numerical examples with various time-varying scenarios is studied.

scholarly journals Active control of liquid film flows: beyond reduced-order models

2021 ◽  
Vol 104 (1) ◽  
pp. 267-287
Author(s):  
Radu Cimpeanu ◽  
Susana N. Gomes ◽  
Demetrios T. Papageorgiou
Keyword(s):  
Liquid Film ◽  
Information Transfer ◽  
Analytical Models ◽  
Feedback Controls ◽  
Reduced Order ◽  
Modelling Framework ◽  
Theoretical Approaches ◽  
Active Feedback ◽  
Feedback Strategies ◽  
Set Up

AbstractThe ability to robustly and efficiently control the dynamics of nonlinear systems lies at the heart of many current technological challenges, ranging from drug delivery systems to ensuring flight safety. Most such scenarios are too complex to tackle directly, and reduced-order modelling is used in order to create viable representations of the target systems. The simplified setting allows for the development of rigorous control theoretical approaches, but the propagation of their effects back up the hierarchy and into real-world systems remains a significant challenge. Using the canonical set-up of a liquid film falling down an inclined plane under the action of active feedback controls in the form of blowing and suction, we develop a multi-level modelling framework containing both analytical models and direct numerical simulations acting as an in silico experimental platform. Constructing strategies at the inexpensive lower levels in the hierarchy, we find that offline control transfer is not viable; however, analytically informed feedback strategies show excellent potential, even far beyond the anticipated range of applicability of the models. The detailed effects of the controls in terms of stability and treatment of nonlinearity are examined in detail in order to gain understanding of the information transfer inside the flows, which can aid transition towards other control-rich frameworks and applications.

Optimization in Trajectory Planning of Multi-Jointed Fingers in Dextrous Hand Designs

1991 ◽  
Author(s):  
A. Meghdari ◽  
H. Sayyaadi
Keyword(s):  
Dynamic Programming ◽  
Motion Control ◽  
Trajectory Planning ◽  
Degrees Of Freedom ◽  
Optimization Technique ◽  
Dynamic Programming Algorithm ◽  
Programming Algorithm ◽  
Kinematics And Dynamics ◽  
Feasible Solutions ◽  
Dextrous Hand

Abstract An optimization technique based on the well known Dynamic Programming Algorithm is applied to the motion control trajectories and path planning of multi-jointed fingers in dextrous hand designs. A three fingered hand with each finger containing four degrees of freedom is considered for analysis. After generating the kinematics and dynamics equations of such a hand, optimum values of the joints torques and velocities are computed such that the finger-tips of the hand are moved through their prescribed trajectories with the least time or/and energy to reach the object being grasped. Finally, optimal as well as feasible solutions for the multi-jointed fingers are identified and the results are presented.

scholarly journals Wavelet multi-resolution approximation of time-varying frame structure

2018 ◽  
Vol 10 (8) ◽  
pp. 168781401879559 ◽  
Author(s):  
Min Xiang ◽  
Feng Xiong ◽  
Yuanfeng Shi ◽  
Kaoshan Dai ◽  
Zhibin Ding
Keyword(s):  
Parameter Estimation ◽  
Degrees Of Freedom ◽  
Structural Parameters ◽  
Identification Problem ◽  
Frame Structure ◽  
Structural Parameter ◽  
Time Varying ◽  
Engineering Structures ◽  
Time Frequency ◽  
Non Parametric

Engineering structures usually exhibit time-varying behavior when subjected to strong excitation or due to material deterioration. This behavior is one of the key properties affecting the structural performance. Hence, reasonable description and timely tracking of time-varying characteristics of engineering structures are necessary for their safety assessment and life-cycle management. Due to its powerful ability of approximating functions in the time–frequency domain, wavelet multi-resolution approximation has been widely applied in the field of parameter estimation. Considering that the damage levels of beams and columns are usually different, identification of time-varying structural parameters of frame structure under seismic excitation using wavelet multi-resolution approximation is studied in this article. A time-varying dynamical model including both the translational and rotational degrees of freedom is established so as to estimate the stiffness coefficients of beams and columns separately. By decomposing each time-varying structural parameter using one wavelet multi-resolution approximation, the time-varying parametric identification problem is transformed into a time-invariant non-parametric one. In solving the high number of regressors in the non-parametric regression program, the modified orthogonal forward regression algorithm is proposed for significant term selection and parameter estimation. This work is demonstrated through numerical examples which consider both gradual variation and abrupt changes in the structural parameters.

scholarly journals Existence and Uniqueness of Solutions for the p(x)-Laplacian Equation with Convection Term

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1768
Author(s):  
Bin-Sheng Wang ◽  
Gang-Ling Hou ◽  
Bin Ge
Keyword(s):  
Existence And Uniqueness ◽  
Variable Exponent ◽  
Convection Term ◽  
Pseudomonotone Operators ◽  
Uniqueness Of Solutions ◽  
Laplacian Equation ◽  
Uniqueness Of The Solution ◽  
Gradient Based ◽  
Surjectivity Result ◽  
Quasilinear Elliptic

In this paper, we consider the existence and uniqueness of solutions for a quasilinear elliptic equation with a variable exponent and a reaction term depending on the gradient. Based on the surjectivity result for pseudomonotone operators, we prove the existence of at least one weak solution of such a problem. Furthermore, we obtain the uniqueness of the solution for the above problem under some considerations. Our results generalize and improve the existing results.

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