Chapter 4 describes the parameter estimation methods for extracting modal properties. A new modal characteristic vector called modal observability vector is introduced. The practical, clear, and concise guide for conducting experimental modal tests. Pdf identification of structural system parameters from dynamic. According to this problem, a doppler aliasing free micromotion parameter estimation method based on the modulo generalized hough transform is proposed in this paper. Pdf automated modal parameter estimation using correlation.
Modal parameter estimation is used, for example, when one wants to extract a partial structural dynamics model in terms of quantities such as eigenvectors, resonant frequencies, damping, and modal mass from test data acquired from a continuum elastic. An iterative hilberthuang transformation hht based algorithm is developed to extract the modal parameters of a linear time invariant lti system excited by recorded nonstationary ground motion. Modal parameter estimation is the process of determining these parameters from experimental data. Determining the accuracy of modal parameter estimation. Prior to the 1970s, most modal parameter estimation was performed using some. Original statistical approach for the reliability in modal. Dynamic model the dynamic behaviour of the structure with ndegree of freedom is explained often with the following dynamic motion equation. A systematic treatment of modal estimation of a wavefront phase from its gradients is given. Modal parameter estimation from ambient data using time. Use of the discrete wavelet transform for the modal parameter estimation is rare and inadequate due to its different.
A study on modal parameter estimation method based on. In the same screen layout, the geometry with dof information is shown together with a graph area for. Mechanical vibrations overview of experimental modal analysis. Quantifying uncertainty in modal parameters estimated.
First, the basics of technical concepts and practical handson performance of an experimental modal. Determining the accuracy of modal parameter estimation methods. Chapter 4 parameter estimation thus far we have concerned ourselves primarily with probability theory. The text draws on the authors extensive experience to cover the practical side of the concerns that may arise when performing an experimental modal test. Modal analysis is used to characterize resonant vibration in machinery and structures. The most common type of modal testing system today uses an fft analyzer to measure a set of frequency response functions frfs from a structure, and then uses a parameter. The function generates one set of natural frequencies and damping ratios for.
Frf data to include in the analysis are easily filtered, sorted and then selected using the data matrix selector table. Parameter estimation can be important even when we are fairly con. Furthermore, a set of modal parameters can completely characterize the dy. Temporal aliasing is a major concern in the sampling of video and audio signals. Recent work with autonomous modal parameter estimation has shown great promise in the quality of the modal parameter estimation results when compared to results from traditional methods by experienced users. Automatic parameter setting of random decrement technique for the estimation of building modal parameters fatima nasser1, zhongyang li1, nadine martin1 and philippe gueguen2 1gipsalab, departement images signal bp 46 961 f38402 saint martin dheres, france fatima. These parameters specify any constants appearing in the model and provide a mechanism for e. As in regression, differences in parameters across conditions help us understand whether and how different cues affect infant multi modal learning. Chapter 1 provides a brief overview of structural dynamics theory.
Estimation of the parameters of an arma model umberto triacca dipartimento di ingegneria e scienze dellinformazione e matematica universit a dellaquila, umberto. Modal parameter estimation is the process of determin ing these parameters from experimental data. The modal parameters of groups of reconstructed signals are identified by datassi, and groups of identification results are obtained. Aliasing can be caused either by the sampling stage or the reconstruction stage.
The identification process consists of estimating the modal parameters from frequency response. If a set of frfs contains modes which are heavily coupled resulting from the combined effect of heavy damping and small modal frequency separation, then an mdof fitter is usually required ade to quately identify the modal parameters. The estimation of modal parameters from a set of noisy measured data is a highly judgmental task, with user expertise playing a significant role in distinguishing between estimated physical and noise modes of a testpiece. Chapter 23 a parameter optimization for mode shapes estimation using kriging interpolation minwoo chang and shamim n. Even limiting the attention to linear systems, it is a matter of fact that both the complexity of the methods and the expectations of the analysts have. Aliasing in modal parameter estimation a historical look and new innovations. Modal parameter extraction is a bit more difficult in operational modal analysis because the stimulus is unknown. For that reason, the algorithms listed above lsce, fdpi, peak picking are not applicable. Modal analysis is defined as the study of the dynamic. Topics include operating data, multiple input multiple course output testing, advanced multiple reference modal parameter estimation, structural. Modal parameter estimation is used, for example, when one wants to extract a partial structural dynamics model in terms of quantities such as eigenvectors, resonant frequencies, damping, and modal mass from test data acquired from a continuum elastic body under certain boundary conditions and excitations. Automated modal parameter estimation using correlation analysis and bootstrap sampling article pdf available in mechanical systems and signal processing 100 july 2017 with 8 reads.
Chapter 2 and 3 which is the bulk of the note describes the measurement process for acquiring frequency response data. Modal parameter estimation is a special case of system identification where the a priori model of the. In the past decades a number of papers dealing with the problem of modal parameters estimation of vibrating structures has been presented 1. May 12, 2011 while some conventional modal parameter estimation tools such as the consistency diagram and the complex mode indicator function cmif look slightly different, the frequencies, damping and mode shapes estimated using afrfs are consistent with those of standard modal analysis. Enough spatial resolution to avoid an aliased view of the mode shapes. It also prevents aliasing of modal characteristics from outofband modes which tend to contaminate. Within this context of properly exciting the structure, modal testing was also known as resonance testing, as it initiated using various shakers properly tuned in order to put the structure into resonance.
Specify a model order of 6 modes and specify physical frequencies for the 3 modes determined from the stabilization diagram. Modal parameters from frequencyresponse functions matlab. Furthermore, a set of modal parameters can completely characterize the dy namic properties of a structure. While autonomous modal parameter estimation means slightly different things to different researchers and practitioners, for the purpose of this discussion, autonomous will require an. How to determine the modal parameters of simple structures the modal parameters of, jil vl i simple structures can be simply established with the aid of a dualchannel signal analyzer type 2032 or 2034. Automated modal parameter estimation using correlation. The estimation of modal parameters from a set of noisy measured data is a highly judgmental task, with user expertise playing a significant role in distinguishing between estimated physical and noise. A rayleigh distribution is often observed when the overall magnitude of. Automatic parameter setting of random decrement technique for. Modal parameter estimation is a special case of system identification where the a priori model of the system is known to be in the form of modal parameters. Chapter p arameter estimation p 1x w 1 p 2x w 2 figure example of image with t w o regions mo delled with t o priors p x and precise parameter estimation at the region b order requires computations in adaptiv e windo ws y 1 y 2 x 0 y n figure a deterministic parameter x observ ed in noisy conditions where n is the noise and y the observ ation. For exper imental data that does not perfectly match the theoretical requirements of the modal parameter estimation algorithms, the choice of what procedure is used to estimate the.
An improved implementation of the orthogonal polynomial modal. Shock and vibration 11 2004 395409 395 ios press the polymax frequencydomain method. Automated modal parameter estimation for operational modal analysis of large systems palle andersen structural vibration solutions as niels jernes. A modal parameter estimation technique for rotating machineries emilio di lorenzo 31, simone manzato 2, bart peeters, frederik vanhollebeke 4, wim desmet 5, and francesco marulo 6 1 research engineer, siemens industry software nv, leuven. Physical modes are identified by coupling the bootstrapping with correlation analysis and a clustering method. Parameter estimation setup the parameter estimation setup task is where you prepare and execute the curvefitting. We introduce a gradient matrix and use it to describe cross coupling of aberrations lack of orthogonality of its column vectors and aliasing of aberrations lack of. This lesson considers three techniques for estimation of the parameters. Modal test and suspension design for the orion launch abort system. In this article, the lms polymax method was used on two historically difficult data sets a trimmed car body high. Presents parameter estimation methods common with discrete probability distributions, which is of particular interest in text modeling. An improved implementation of the orthogonal polynomial modal parameter estimation algorithm using the orthogonal complement.
Review of spatial domain modal parameter estimation procedures. This is useful only in the case where we know the precise model family and parameter values for the situation of interest. Problems of spatial aliasing and nonunique eigenvectors of coalescent. Some practical tools for the parameter estimation process in general are referenced andor. Modal analysis is an essential technology behind solving todays noise and vibration problems. Much less talked about is the aliasing that occurs in modal parameter estimation, or curvefitting, when the residual effects of outofband modes violate assumptions of the finite dimensional parametric model that the experimentalist uses to curvefit the acquired digitized data.
Its basic idea is to search and match the parameters of. Original statistical approach for the reliability in modal parameters estimation imacxxvii joseph morlier, boris chermain, yves gourinat. Based on the improved accuracy of the parameter estimates and the availability. Inter nal to the software implementation, choices are available to estimate the scaled modal vectors and modal scaling in a number of ways. Quantitative linking hypotheses for infant eye movements. A novel automated modal parameter estimation algorithm is developed. A mode of vibration is defined by three parameters. Us20090204355a1 methods and apparatus for modal parameter.
Modal parameter estimation, or modal identification, is a special case of system identification where the a priori model of the system is known to be in the form of modal parameters. This course focuses on the practical implementation of experimental modal analysis testing. Application notes how to determine the modal parameters. In probability theory and statistics, the rayleigh distribution is a continuous probability distribution for nonnegativevalued random variables. Spatial aliasing b due to limited spatial resolution and induce loss of details. Autonomous modal parameter estimation the interest in automatic modal parameter estimation methods has been documented in the literature since at least the mid 1960s when the primary modal method was the analog, force appropriation method. The current approach in modal function frf measurements.
Spatial information in autonomous modal parameter estimation. Automated modal parameter estimation using correlation analysis and bootstrap sampling vahid yaghoubi, majid k. This course focuses on additional test and analysis tools beyond those presented in the basic modal analysis. Parameter estimation for linear dynamical systems with applications to experimental modal analysis in this study the fundamentals of structural dynamics and system identi. On moving average parameter estimation niclas sandgren. As part of the imac technology center display a mrit was performed on a simple hframe structure and quick cmif analysis was. H1 estimator 1 represented by following formulation in laplace domain is a commonly used method for estimating frfs from the measured data. First, two kinds of mode shape estimation methods, herein referred to as the quadrature peaks. Not surprisingly, the allimportant quantity r 0 is frequently the focus of considerable parameter estimation effort. Institute of structural engineering identi cation methods for structural systems 11. Modal excitation 2 intoduction the presentation is concerned with a short tutorial on modal excitation.
Application of modal scaling to the pole selection phase. Pakzad abstract a parametric study of kriging interpolation for optimal sensor placement osp is presented in this paper. Types of methods force appropriation methods normal mode. How can methods of linear prediction and approximate least squares be extended to modal analysis from sparsely sampled data. We adapt methods of linear prediction and approximate least squares for estimating the parameters from sparse and coprime arrays in a modal analysis problem. Various methods have been developed to automate this procedure.
Automated modal parameter estimation for operational. Modal analysis theory and testing ward heylen stefan lammens paul sas division of production engineering, machine design and automation katholieke universiteit leuven. The switched capacitor filter acted as a tracking antialiasing filter. Parameter estimation this lecture nonparametric density estimation the next two lectures parameter estimation assume a particular form for the density e. Application and evaluation of multiple input modal parameter estimation. Modal analysis is a strong and reliable vibration analysis tool used in modern engineering. Modal parameter estimation methods are used to obtain modal.
A practitioners guide outlines the basic information necessary to conduct an experimental modal test. In addition, the results of each group include the corresponding frequency value, damping ratio, and mode coefficient. To infer parameter values, we perform bayesian inference in the model specified in figure 1. Based on the measuredsynthesized frf dynamic parameters of the structures considered could be obtained in this study basics of the experimental modal analysis is studied. Imacxxvi modal excitation 57 before release of test item at the conclusion of data acquisition phase a quick reduction of the data using a simple modal parameter estimation process should be performed. Aalborg universitet automated modal parameter estimation. Application and evaluation of multiple input modal parameter estimation article pdf available january 1987 with 55 reads how we measure reads. Approaches to parameter estimation before discussing the bayesian approach to parameter estimation it is important to understand the classical frequentest.
Instead, a new algorithm is introduced called stochastic subspace identification ssi. Parameter estimation from compressed and sparse measurements. Much less talked about is the aliasing that occurs in modal parameter estimation, or curvefitting, when the residual effects of out of band modes violate the assumptions of the finite dimensional parametric model that the experimentalist uses to curvefit the acquired digitized data. To overcome this problem, this study presents an algorithm for autonomous modal parameter estimation in which the only required optimization is performed in a threedimensional space. However, microdoppler is usually too significant to result in aliasing in the terahertz band. Online intelligent identification of modal parameters for. Phillips university of cincinnati, department of mechanical engineering, cincinnati, ohio, 45221, usa abstract acoustic modal analysis ama is of interest in cases where accelerometer measurements are limited by. Estimation of modal parameters and their uncertainty. Modal parameters include the complexvalued modal frequencies.
A doppler aliasing free micromotion parameter estimation. Frfs are calculated based on the measured data in modal experiment and it is main input to the modal parameter estimation. Avoiding modal aliasing when analyzing responses with partial. Application of modal parameter estimation methods for continuous. Pdf modal parameter estimation of lti system using. Modal parameter estimation using acoustic modal analysis. Abrahamsson department of applied mechanics, chalmers university of technology, gothenburg, sweden abstract the estimation of modal parameters from a set of noisy measured data is a highly judgmental task. The estimation of modal parameters from a set of noisy measured data is a highly judgmental task, with user expertise playing a significant role in distinguishing between estimated physical and. Modal test and suspension design for the orion launch. Cross coupling and aliasing in modal wavefront estimation. Pdf application and evaluation of multiple input modal. Aliasing in 2d mapping a continuous function to a discrete one is called sampling. Modal parameter estimation using acoustic modal analysis w. Use estimation commands like ssest or tfest to create sys starting from a measured frequencyresponse function or from timedomain input and output signals.
Cookbook, turn the crank method optimal for large data sizes disadvantages of ml estimation not optimal for small sample sizes can be computationally challenging numerical methods tutorial on estimation and multivariate gaussiansstat 27725cmsc 25400. It is essentially a chi distribution with two degrees of freedom. Parameter estimation techniques that can be used to determine modal parameters frequency, damping, and mode shape from experimentally measured frequency response or unit impulse response are presented with respect to practical implementation and use. Automated modal parameter estimation for operational modal. Then some fundamental parameter estimation algorithms in the literature are provided. To this end, a subspacebased identification method is employed for the estimation and a noniterative correlationbased method is used for the clustering.
1463 1024 1416 1247 1185 1046 789 415 824 332 1222 783 347 1306 136 679 80 670 254 799 1032 1195 218 1160 502 268 244 1403 909 17 1437 268 270 718 13 1188 1161 850 420 1142 1420 1195