Automated modal parameter estimation using correlation analysis and bootstrap sampling vahid yaghoubi, majid k. 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 using correlation analysis and bootstrap sampling article pdf available in mechanical systems and signal processing 100 july 2017 with 8 reads. Aalborg universitet automated modal parameter estimation. Modal parameter estimation is a special case of system identification where the a priori model of the. 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. 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. Parameter estimation can be important even when we are fairly con. How can methods of linear prediction and approximate least squares be extended to modal analysis from sparsely sampled data.
Shock and vibration 11 2004 395409 395 ios press the polymax frequencydomain method. These parameters specify any constants appearing in the model and provide a mechanism for e. 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. Modal analysis is a strong and reliable vibration analysis tool used in modern engineering. 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. It also prevents aliasing of modal characteristics from outofband modes which tend to contaminate. Parameter estimation from compressed and sparse measurements. Determining the accuracy of modal parameter estimation. This course focuses on the practical implementation of experimental modal analysis testing. Prior to the 1970s, most modal parameter estimation was performed using some. 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. A systematic treatment of modal estimation of a wavefront phase from its gradients is given. Modal parameter estimation using acoustic modal analysis w.
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. Use estimation commands like ssest or tfest to create sys starting from a measured frequencyresponse function or from timedomain input and output signals. The switched capacitor filter acted as a tracking antialiasing filter. A novel automated modal parameter estimation algorithm is developed. Quantifying uncertainty in modal parameters estimated. 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.
Determining the accuracy of modal parameter estimation methods. Cross coupling and aliasing in modal wavefront estimation. To infer parameter values, we perform bayesian inference in the model specified in figure 1. Parameter estimation setup the parameter estimation setup task is where you prepare and execute the curvefitting. Aliasing can be caused either by the sampling stage or the reconstruction stage. As part of the imac technology center display a mrit was performed on a simple hframe structure and quick cmif analysis was. Frfs are calculated based on the measured data in modal experiment and it is main input to the modal parameter estimation. 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. Chapter 1 provides a brief overview of structural dynamics theory. Modal parameter extraction is a bit more difficult in operational modal analysis because the stimulus is unknown. As in regression, differences in parameters across conditions help us understand whether and how different cues affect infant multi modal learning.
Pdf identification of structural system parameters from dynamic. Original statistical approach for the reliability in modal parameters estimation imacxxvii joseph morlier, boris chermain, yves gourinat. Types of methods force appropriation methods normal mode. 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. Original statistical approach for the reliability in modal. Various methods have been developed to automate this procedure. Estimation of the parameters of an arma model umberto triacca dipartimento di ingegneria e scienze dellinformazione e matematica universit a dellaquila, umberto. 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 defined as the study of the dynamic. Dynamic model the dynamic behaviour of the structure with ndegree of freedom is explained often with the following dynamic motion equation. Application and evaluation of multiple input modal parameter estimation.
Chapter 4 describes the parameter estimation methods for extracting modal properties. 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. An improved implementation of the orthogonal polynomial modal parameter estimation algorithm using the orthogonal complement. 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. Frf data to include in the analysis are easily filtered, sorted and then selected using the data matrix selector table. It is essentially a chi distribution with two degrees of freedom. 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. Review of spatial domain modal parameter estimation procedures. While autonomous modal parameter estimation means slightly different things to different researchers and practitioners, for the purpose of this discussion, autonomous will require an. Automatic parameter setting of random decrement technique for. Modal analysis theory and testing ward heylen stefan lammens paul sas division of production engineering, machine design and automation katholieke universiteit leuven. 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. Chapter 23 a parameter optimization for mode shapes. Spatial information in autonomous modal parameter estimation.
In probability theory and statistics, the rayleigh distribution is a continuous probability distribution for nonnegativevalued random variables. Modal parameter estimation is the process of determin ing these parameters from experimental data. This course focuses on additional test and analysis tools beyond those presented in the basic modal analysis. Avoiding modal aliasing when analyzing responses with partial. An improved implementation of the orthogonal polynomial modal. Modal parameter estimation methods are used to obtain modal.
Chapter 2 and 3 which is the bulk of the note describes the measurement process for acquiring frequency response data. A new modal characteristic vector called modal observability vector is introduced. A doppler aliasing free micromotion parameter estimation. Online intelligent identification of modal parameters for. Parameter estimation for linear dynamical systems with applications to experimental modal analysis in this study the fundamentals of structural dynamics and system identi. The current approach in modal function frf measurements. Aliasing in modal parameter estimation a historical look and new innovations. Application of modal scaling to the pole selection phase. Specify a model order of 6 modes and specify physical frequencies for the 3 modes determined from the stabilization diagram.
Its basic idea is to search and match the parameters of. First, the basics of technical concepts and practical handson performance of an experimental modal. Application notes how to determine the modal parameters. Modal parameter estimation using acoustic modal analysis. Parameter estimation this lecture nonparametric density estimation the next two lectures parameter estimation assume a particular form for the density e. H1 estimator 1 represented by following formulation in laplace domain is a commonly used method for estimating frfs from the measured data. Pdf automated modal parameter estimation using correlation.
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. Use of the discrete wavelet transform for the modal parameter estimation is rare and inadequate due to its different. Based on the improved accuracy of the parameter estimates and the availability. A mode of vibration is defined by three parameters. According to this problem, a doppler aliasing free micromotion parameter estimation method based on the modulo generalized hough transform is proposed in this paper. The function generates one set of natural frequencies and damping ratios for. Application and evaluation of multiple input modal parameter estimation article pdf available january 1987 with 55 reads how we measure reads. Compute the modal parameters using the leastsquares complex exponential lsce algorithm. Automated modal parameter estimation for operational. Modal test and suspension design for the orion launch. Chapter 23 a parameter optimization for mode shapes estimation using kriging interpolation minwoo chang and shamim n. Then some fundamental parameter estimation algorithms in the literature are provided. Automated modal parameter estimation for operational modal.
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. 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. Problems of spatial aliasing and nonunique eigenvectors of coalescent. 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. 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. Pakzad abstract a parametric study of kriging interpolation for optimal sensor placement osp is presented in this paper. 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. Physical modes are identified by coupling the bootstrapping with correlation analysis and a clustering method. A practitioners guide outlines the basic information necessary to conduct an experimental modal test. For that reason, the algorithms listed above lsce, fdpi, peak picking are not applicable. Topics include operating data, multiple input multiple course output testing, advanced multiple reference modal parameter estimation, structural. Pdf modal parameter estimation of lti system using. 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.
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. In addition, the results of each group include the corresponding frequency value, damping ratio, and mode coefficient. Furthermore, a set of modal parameters can completely characterize the dy namic properties of a structure. This is useful only in the case where we know the precise model family and parameter values for the situation of interest. 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.
Enough spatial resolution to avoid an aliased view of the mode shapes. Institute of structural engineering identi cation methods for structural systems 11. Automated modal parameter estimation for operational modal analysis of large systems palle andersen structural vibration solutions as niels jernes. Some practical tools for the parameter estimation process in general are referenced andor. 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. 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. To this end, a subspacebased identification method is employed for the estimation and a noniterative correlationbased method is used for the clustering. Pdf application and evaluation of multiple input modal. Modal analysis is an essential technology behind solving todays noise and vibration problems. Aliasing in 2d mapping a continuous function to a discrete one is called sampling. Modal parameter estimation from ambient data using time. Estimation of modal parameters and their uncertainty.
Spatial aliasing b due to limited spatial resolution and induce loss of details. 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. In the past decades a number of papers dealing with the problem of modal parameters estimation of vibrating structures has been presented 1. Modal parameters from frequencyresponse functions matlab.
Not surprisingly, the allimportant quantity r 0 is frequently the focus of considerable parameter estimation effort. Modal test and suspension design for the orion launch abort system. 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. Temporal aliasing is a major concern in the sampling of video and audio signals. We adapt methods of linear prediction and approximate least squares for estimating the parameters from sparse and coprime arrays in a modal analysis problem. The identification process consists of estimating the modal parameters from frequency response. Inter nal to the software implementation, choices are available to estimate the scaled modal vectors and modal scaling in a number of ways. A rayleigh distribution is often observed when the overall magnitude of. 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. 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.
However, microdoppler is usually too significant to result in aliasing in the terahertz band. Furthermore, a set of modal parameters can completely characterize the dy. Quantitative linking hypotheses for infant eye movements. Modal excitation 2 intoduction the presentation is concerned with a short tutorial on modal excitation. First, two kinds of mode shape estimation methods, herein referred to as the quadrature peaks. In this article, the lms polymax method was used on two historically difficult data sets a trimmed car body high.
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. The modal parameters of groups of reconstructed signals are identified by datassi, and groups of identification results are obtained. 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. Original statistical approach for the reliability in modal parameters.
Instead, a new algorithm is introduced called stochastic subspace identification ssi. Chapter 4 parameter estimation thus far we have concerned ourselves primarily with probability theory. On moving average parameter estimation niclas sandgren. Us20090204355a1 methods and apparatus for modal parameter. Approaches to parameter estimation before discussing the bayesian approach to parameter estimation it is important to understand the classical frequentest. Modal analysis is used to characterize resonant vibration in machinery and structures. Modal parameters include the complexvalued modal frequencies.
Modal parameter estimation is the process of determining these parameters from experimental data. Application of modal parameter estimation methods for continuous. Presents parameter estimation methods common with discrete probability distributions, which is of particular interest in text modeling. The practical, clear, and concise guide for conducting experimental modal tests.
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