scholarly journals Prediction of Modal Parameters of Linear Time-Varying Systems

2010 ◽  
Vol 17 (4-5) ◽  
pp. 483-490 ◽  
Author(s):  
S. Marchesiello ◽  
A. Bellino ◽  
L. Garibaldi
Keyword(s):  
Stochastic Systems ◽  
Linear Time ◽  
State Space Model ◽  
Modal Parameters ◽  
Time Varying ◽  
Engineering Structures ◽  
Angle Variation ◽  
Linear Time Invariant ◽  
Stochastic Subspace Identification ◽  
Robotic Devices

Many engineering structures, such as cranes, traffic-excited bridges, flexible mechanisms and robotic devices exhibit characteristics that vary with time and are referred to as time-varying or nonstationary. In particular, linear time-varying (LTV) systems have been often dealt with on a case-by-case basis. Many concepts and analytic methods of linear time-invariant (LTI) systems cannot be applied to LTV systems, as for example the conventional definition of modal parameters. In fact, LTV systems violate one of the assumptions of the conventional modal analysis, which is stationarity.Subspace-based identification methods, proposed in the 1970s, have been attracting much attention due to their affinity to the modern control theory, which is based on the state space model. These methods are now successfully applied to many industrial cases and may be considered reference methods for identifying LTI systems.In this paper the use of a subspace-based method for identifying LTV systems is discussed and applied to both numerical and experimental systems. More precisely a modified version of the SSI method, referred to here as ST-SSI (Short Time Stochastic Subspace Identification) is introduced as well as a method for predicting time-varying stochastic systems using the angle variation between the subspaces; the latter is able to predict the system parameter in the “near” future.

A Method for Modal Parameter Identification of Time Varying Vibration Systems

2012 ◽  
Vol 479-481 ◽  
pp. 688-693
Author(s):  
Zi Ying Wu ◽  
Kun Shi
Keyword(s):  
Linear Time ◽  
Least Square Method ◽  
Degree Of Freedom ◽  
Least Square ◽  
Modal Parameters ◽  
Time Varying ◽  
Recursive Least Square ◽  
Modal Parameter ◽  
Linear Time Invariant ◽  
Prony Method

In this paper a new time varying multivariate Prony (TVM-Prony) method is put forward to identify modal parameters of time varying (TV) multiple-degree-of-freedom systems from measured vibration responses. The proposed method is based on the classical Prony method that is often used to identify modal parameters of linear time invariant systems. The main advantage of the propose approach is that it can analyze multi-dimensional nonstationary signals simultaneously. A modified recursive least square method based on the traditional one is presented to determine the TV coefficient matrices of the multivariate parametric model established in the proposed method. The efficiency and accuracy of the identification approach is demonstrated by a numerical example, in which a TV mass-string system with three-degree-of-freedom is investigated. Satisfied results are obtained.

Optimal Nonlinear Estimation of Linear Stochastic Systems: The Multivariable Extension

1996 ◽  
Vol 118 (2) ◽  
pp. 350-353 ◽  
Author(s):  
M. A. Hopkins ◽  
H. F. VanLandingham
Keyword(s):  
Stochastic Systems ◽  
Transfer Functions ◽  
Mimo Systems ◽  
Linear Time ◽  
Nonlinear Method ◽  
Single Input Single Output ◽  
Linear Time Invariant ◽  
Single Output ◽  
Time Invariant ◽  
Time Systems

This paper extends to multi-input multi-output (MIMO) systems a nonlinear method of simultaneous parameter and state estimation that appeared in the ASME JDSM&C (September, 1994), for single-input single-output (SISO) systems. The method is called pseudo-linear identification (PLID), and applies to stochastic linear time-invariant discrete-time systems. No assumptions are required about pole or zero locations; nor about relative degree, except that the system transfer functions must be strictly proper. In the earlier paper, proofs of optimality and convergence were given. Extensions of those proofs to the MIMO case are also given here.

scholarly journals FE Analysis of Communications Systems for Drive-Thru Restaurants in a Business Dispute Over Specifications and Design Process

2021 ◽  
Vol 38 (1) ◽  
Author(s):  
Robert Peruzzi
Keyword(s):  
Communication System ◽  
Communication Systems ◽  
Linear Time ◽  
Forensic Analysis ◽  
Time Varying ◽  
Audio Quality ◽  
Linear Time Invariant ◽  
Linear Time Invariant Systems ◽  
Quick Service ◽  
Time Invariant

Forensic analysis in this case involves the design of a communication system intended for use in Quick Service Restaurant (QSR) drive-thru lanes. This paper provides an overview of QSR communication system components and operation and introduces communication systems and channels. This paper provides an overview of non-linear, time-varying system design as contrasted with linear, time-invariant systems and discusses best design practices. It also provides the details of how audio quality was defined and compared for two potentially competing systems. Conclusions include that one of the systems was clearly inferior to the other — mainly due to not following design techniques that were available at the time of the project.

Linear Approximations for Swing Leg Motion During Gait

1984 ◽  
Vol 106 (2) ◽  
pp. 137-143 ◽  
Author(s):  
W. H. Lee ◽  
J. M. Mansour
Keyword(s):  
Linear Systems ◽  
System Analysis ◽  
Linear Time ◽  
Time Varying ◽  
Two Dimensional ◽  
State Variables ◽  
Linear Time Invariant ◽  
Linear Time Invariant Systems ◽  
Leg Motion ◽  
Time Invariant

The applicability of a linear systems analysis of two-dimensional swing leg motion was investigated. Two different linear systems were developed. A linear time-varying system was developed by linearizing the nonlinear equations describing swing leg motion about a set of nominal system and control trajectories. Linear time invariant systems were developed by linearizing about three different fixed limb positions. Simulations of swing leg motion were performed with each of these linear systems. These simulations were compared to previously performed nonlinear simulations of two-dimensional swing leg motion and the actual subject motion. Additionally, a linear system analysis was used to gain some insight into the interdependency of the state variables and controls. It was shown that the linear time varying approximation yielded an accurate representation of limb motion for the thigh and shank but with diminished accuracy for the foot. In contrast, all the linear time invariant systems, if used to simulate more than a quarter of the swing phase, yielded generally inaccurate results for thigh shank and foot motion.

scholarly journals Time-Varying Vector Norm and Lower and Upper Bounds on the Solutions of Uniformly Asymptotically Stable Linear Systems

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 915
Author(s):  
Robert Vrabel
Keyword(s):  
Linear Systems ◽  
Linear Time ◽  
Upper Bounds ◽  
Time Varying ◽  
Asymptotically Stable ◽  
Lower And Upper Bounds ◽  
Linear Time Invariant ◽  
Vector Norm ◽  
Linear Time Invariant Systems ◽  
Stable Linear

Based on the eigenvalue idea and the time-varying weighted vector norm in the state space R n we construct here the lower and upper bounds of the solutions of uniformly asymptotically stable linear systems. We generalize the known results for the linear time-invariant systems to the linear time-varying ones.

Floquet Experimental Modal Analysis for System Identification of Linear Time-Periodic Systems

2007 ◽  
Author(s):  
Matthew S. Allen
Keyword(s):  
System Identification ◽  
Linear Time ◽  
Time Varying ◽  
Response Model ◽  
State Matrix ◽  
Linear Time Invariant ◽  
Response Data ◽  
Time Varying Systems ◽  
Time Invariant ◽  
Time Periodic

A variety of systems can be faithfully modeled as linear with coefficients that vary periodically with time or Linear Time-Periodic (LTP). Examples include anisotropic rotorbearing systems, wind turbines, satellite systems, etc… A number of powerful techniques have been presented in the past few decades, so that one might expect to model or control an LTP system with relative ease compared to time varying systems in general. However, few, if any, methods exist for experimentally characterizing LTP systems. This work seeks to produce a set of tools that can be used to characterize LTP systems completely through experiment. While such an approach is commonplace for LTI systems, all current methods for time varying systems require either that the system parameters vary slowly with time or else simply identify a few parameters of a pre-defined model to response data. A previous work presented two methods by which system identification techniques for linear time invariant (LTI) systems could be used to identify a response model for an LTP system from free response data. One of these allows the system’s model order to be determined exactly as if the system were linear time-invariant. This work presents a means whereby the response model identified in the previous work can be used to generate the full state transition matrix and the underlying time varying state matrix from an identified LTP response model and illustrates the entire system-identification process using simulated response data for a Jeffcott rotor in anisotropic bearings.

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