Polyreference Time Domain Research Articles

Comparison of Different Estimation Algorithms Used in the Experimental Determination of Modal Parameters

The paper deals with the estimation of modal parameters and its main purpose is to compare differences in the values of natural frequencies and damping ratios, which were estimated using three different extraction methods: Rational Fraction Polynomial method, Complex Mode Indicator Function and Polyreference Time Domain Technique. These methods are well suited to the more general application to multi-FRF data, both of the SIMO and the MIMO types. The object of measurement was a freely suspended steel rod of circular cross section. The responses of the analyzed structure were measured by accelerometer and laser vibrometer. The results of these measurements are also discussed in the paper.

Using the unified matrix polynomial approach (UMPA) for the development of the stochastic subspace identification (SSI) algorithm

The unified matrix polynomial approach (UMPA) was developed in order to understand and derive various experimental modal analysis algorithms (which have been developed in isolation) using a common mathematical formulation. Various commercially available algorithms – such as the polyreference time domain, least squares complex exponential, and eigensystem realization algorithm etc. – can be explained using UMPA methodology, which makes it easier to understand both the advantages and limitations of such algorithms. In view of this fundamental characteristic of the UMPA, this paper aims at using the approach to understand, explain and develop the stochastic subspace identification (SSI) algorithm - a popular time domain operational modal analysis (OMA) algorithm. The roots of SSI algorithm lie in the identification of linear dynamic systems, traditionally a communications and controls engineering area. By means of the UMPA, the SSI algorithm’s similarity to a high order time domain OMA algorithm can be shown. It can also be shown that state transition matrices identified using the SSI algorithm and UMPA formulation are related to each other through a similarity transformation, thus characterizing the same system.

Improved polyreference time domain method for modal identification using local or global noise removal techniques

Modal identification involves estimating the modal parameters, such as modal frequencies, damping ratios, and mode shapes, of a structural system from measured data. Under the condition that noisy impulse response signals associated with multiple input and output locations have been measured, the primary objective of this study is to apply the local or global noise removal technique for improving the modal identification based on the polyreference time domain (PTD) method. While the traditional PTD method improves modal parameter estimation by over-specifying the computational model order to absorb noise, this paper proposes an approach using the actual system order as the computational model order and rejecting much noise prior to performing modal parameter estimation algorithms. Two noise removal approaches are investigated: a “local” approach which removes noise from one signal at a time, and a “global” approach which removes the noise of multiple measured signals simultaneously. The numerical investigation in this article is based on experimental measurements from two test setups: a cantilever beam with 3 inputs and 10 outputs, and a hanged plate with 4 inputs and 32 outputs. This paper demonstrates that the proposed noise-rejection method outperforms the traditional noise-absorption PTD method in several crucial aspects.

ModalCAD—Interactive Dynamic Characteristic Identification Software for Experimental and Operational Modal Analysis of Engineering Structures

Abstract In this paper the development of interactive and comparative dynamic characteristic identification software titled as the ModalCAD is described. The software is developed for vibration monitoring of civil engineering structures and constructed by using MATLAB, which is a mathematical tool developed by The Mathworks. The modal analysis of structures consists of four distinct steps: Data collection, digital signal processing, determination of the modal parameters (eigenfrequencies, damping ratios, mode shapes, and modal scaling factors) with modal data presentation/validation and model updating. The ModalCAD software is a powerful tool that deals with modal parameter identification and validation procedure. The ModalCAD offers extensive functionalities for the visualization and processing of the measurement data, the identification of system models, and the determination and visualization of the structure’s modal parameters. The program disposes of a graphical user interface, which what makes it very intuitive and easy to handle. The most common modal parameter estimation techniques have been used in the ModalCAD. The Operating Vectors method, Complex Exponential method, and Polyreference Time Domain method are implemented in a user-friendly way. By pushing buttons the user is guided through the whole process of input-output and output-only modal analysis: Preprocessing the data, system identification, extracting modal parameters, animating mode shapes, and evaluating model validation tools. The possibilities of the program are demonstrated with a three dimensional frame model. It can be said that the ModalCAD software can be used as a scientific tool in future structural health monitoring studies of researchers.

Modal Analysis Using Operating Modal Identification Method

Sometimes it is very difficult for some large scale operating structures to measure the input forces. Modal parameters must be estimated on response only. A poly-reference time domain operating modal identification complex exponential method is presented since cross-correlation functions have the same form as impulse response functions. Then a poly-reference frequency domain operating modal identification method is proposed in this paper. An experiment on an aircraft model is performed to verify the proposed schemes. The results show that both outlined schemes can extract the parameters from output-only and the modal parameters extracted by proposed frequency-domain method are more accurate than those by presented time domain complex exponential method.

Developments and Comparisons on the Definition of an Instantaneous Damping Estimator for Structures under Natural Excitation

Accurate identification of damping constitutes a relevant issue for structural health monitoring. In fact, high modal or localized damping ratios are often associated with the presence of structural damage. This question may become even more challenging when identifying a structure from its natural vibration (due to wind, traffic etc.). This article describes the results of the latest studies, conducted by this research group, focusing on the definition of an instantaneous estimator of damping for the identification of structures under unknown non-stationary excitation. A method is presented, in particular, which is based on instantaneous curve-fitting applied directly to time-frequency representations of dynamic response signals. One of the strong points of this technique is its flexibility: from each signal, in fact, a time function of damping is extracted, providing punctual information on estimate stability. A series of numerical applications to Multiple Degree of Freedom (M-DOF) systems is presented; the performance of the method is examined under increasing levels of non stationarity of the excitation. Finally, the results are compared with those obtained, on the same data, through the use of three known time-domain identification methods: Direct System Parameter Identification (DSPI), Eigensystem Realisation Algorithm (ERA), Polyreference Time Domain (PRTD). The latter two were used with the Random Decrement function.

Stochastic System Identification for Operational Modal Analysis: A Review

This paper reviews stochastic system identification methods that have been used to estimate the modal parameters of vibrating structures in operational conditions. It is found that many classical input-output methods have an output-only counterpart. For instance, the Complex Mode Indication Function (CMIF) can be applied both to Frequency Response Functions and output power and cross spectra. The Polyreference Time Domain (PTD) method applied to impulse responses is similar to the Instrumental Variable (IV) method applied to output covariances. The Eigensystem Realization Algorithm (ERA) is equivalent to stochastic subspace identification.

A UNIFIED MATRIX POLYNOMIAL APPROACH TO MODAL IDENTIFICATION

One important current focus of modal identification is a reformulation of modal parameter estimation algorithms into a single, consistent mathematical formulation with a corresponding set of definitions and unifying concepts. Particularly, a matrix polynomial approach is used to unify the presentation with respect to current algorithms such as the least-squares complex exponential (LSCE), the polyreference time domain (PTD), Ibrahim time domain (ITD), eigensystem realization algorithm (ERA), rational fraction polynomial (RFP), polyreference frequency domain (PFD) and the complex mode indication function (CMIF) methods. Using this unified matrix polynomial approach (UMPA) allows a discussion of the similarities and differences of the commonly used methods. the use of least squares (LS), total least squares (TLS), double least squares (DLS) and singular value decomposition (SVD) methods is discussed in order to take advantage of redundant measurement data. Eigenvalue and SVD transformation methods are utilized to reduce the effective size of the resulting eigenvalue–eigenvector problem as well.

Application of Singular-Value Decomposition for Structural Modal Analysis

This paper presents the methods of singular-value decomposition and pseudoinverse to refine the original polyreference time domain (PRTD) modal parameter identification algorithm. The automatic determination of the number of physical modes over the desired frequency range is strongly addressed. Meanwhile, distinguishing between the physical and computational modes is achieved through the modified modal assurance criterion. To evaluate the effectiveness of this method, two test cases were constructed. Verification results show that the current method yields a very good improvement of the PRTD method.

Time Domain Parameter Identification Methods for Linear Modal Analysis: A Unifying Approach

The paper describes a method that uses a multivariate model in the form of a nonhomogeneous finite difference equation to identify modal parameters of a mechanical structure. The modal parameters of this equation are estimable using a model that involves multiple input, multiple output vibration data. Thus, improved global estimates of modal parameters can be obtained, including the identification of highly coupled and pseudo-repeated modes of vibration. When the data are in the form of impulse or free decay responses, then the parameters of the homogeneous part of the equation can be estimated separately, and the method is then related to the Least Squares Complex Exponential method, the Polyreference Time Domain method and the Ibrahim Time Domain method.