On the problem of stochastic experimental modal analysis based on multiple-excitation multiple-response data, part II: The modal analysis approach

In this part of the paper the stochastic multiple-excitation multiple-response experimental modal analysis problem is considered. The relationship between the actual structural and noise dynamics and their discrete special-form ARMAX-type representation is studied for each one of the vibration displacement, velocity and acceleration data cases, and a novel and effective modal analysis approach is introduced that, unlike previous schemes, is capable of operating on any one of these types of data records. By accounting for issues such as the required excitation signal type and stochastic model form, algorithmic instability occurrence and other well-known estimation difficulties, model structure estimation and model validation, as well as model reduction and analysis based on the dispersion analysis methodology introduced in the first part of the paper [1], the proposed approach not only overcomes the limitations and drawbacks of current schemes but also constitutes the first comprehensive procedure for stochastic multiple-excitation multiple-response experimental modal analysis.The effectiveness of the approach is demonstrated through numerical experiments with structural systems characterized by well-separated and closely spaced modes, and data records of various lengths and signal-to-noise ratios. Comparisons with the classical frequency domain method and the deterministic eigensystem realization algorithm are also made, and the approach is finally used for the experimental modal analysis of a three-span beam from laboratory data.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/30969/1/0000642.pd

On the problem of stochastic experimental modal analysis based on multiple-excitation multiple-response data, part I: Dispersion analysis of continuous-time structural systems

Despite its importance and the undisputable significance of stochastic effects, the problem of multiple-excitation multiple-response experimental modal analysis has thus far been almost exclusively considered within a deterministic framework. In this paper a novel, comprehensive and effective stochastic approach, that, unlike alternative schemes, can operate on vibration displacement, velocity or acceleration data, is introduced. The proposed approach is capable of effectively dealing with noise-corrupted vibration data, while also being characterized by unique features that enable it to overcome major drawbacks of current modal analysis methods and achieve high performance characteristics by employing: (a) proper and mutually compatible force excitation signal type and stochastic model forms, (b) an estimation scheme that circumvents problems such as algorithmic instability, wrong convergence, and high computational complexity, while requiring no initial guess parameter values, (c) effective model structure estimation and model validation procedures, and, (d) appropriate model transformation, reduction and analysis procedures based on a novel dispersion analysis methodology.This dispersion analysis methodology is a physically meaningful way of assessing the relative importance of the estimated vibrational modes based on their contributions ("dispersions") to the vibration signal energy. The effects of modal cross-correlations are fully accounted for, physical interpretations are provided in both the correlation and spectral domains, and the phenomenon of negative dispersion modes is investigated and physically interpreted. The effectiveness of the proposed approach is finally verified via numerical and laboratory experiments, as well as comparisons with the classical frequency domain method and the deterministic eigensystem realization algorithm (ERA).The paper is divided into two parts: the proposed dispersion analysis methodology is introduced in the first one; whereas the complete stochastic experimental modal analysis approach is presented in the second [23].Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/30968/1/0000641.pd

Maximum likelihood identification of stochastic Weiner-Hammerstein-type non-linear systems

The identification problem for non-linear Wiener-Hammerstein-type systems is considered. Unlike alternative techniques that are based on deterministic system representations, a stochastic model structure that explicitly accounts for both the input-output and noise dynamics is postulated. The uniqueness properties of this structure are analysed, and appropriate necessary and sufficient conditions derived. A new time-domain identification method based on the Maximum Likelihood principle is then introduced. Unlike alternative approaches that are mainly in the frequency and correlation domains, the proposed method offers statistically optimal estimates from a single record of normal operating data, and is capable of operating directly on the time-domain data and overcoming errors associated with the evaluation of correlation functions/Fourier transforms or multi-stage procedures. The effectiveness and accuracy of the proposed method are verified via numerical simulations with a number of different systems and noise to signal ratios.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/30169/1/0000554.pd

Identification of dynamic myoelectric signal-to-force models during isometric lumbar muscle contractions

A 14-muscle myoelectric signal (MES)-driven muscle force prediction model of the L3-L4 cross section is developed which includes a dynamic MES-force relationship and allows for cocontraction. Model parameters are estimated from MES and moments data recorded during rapid exertions in trunk flexion, extension, lateral bending and axial twist. Nine young healthy males participated in the experimental testing. The model used in the parameter estimation is of the output error type. Consistent and physically feasible parameter estimates were obtained by normalizing the RMS MES to maximum exertion levels and using nonlinear constrained optimization to minimize a cost function consisting of the trace of the output error covariance matrix. Model performance was evaluated by comparing measured and MES-predicted moments over a series of slow and rapid exertions. Moment prediction errors were on the order of 25, 30 and 40% during attempted trunk flexion-extensions, lateral bends and axial twists, respectively. The model and parameter estimation methods developed provide a means to estimate lumbar muscle and spine loads, as well as to empirically investigate the use and effects of cocontraction during physical task performances.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/31486/1/0000408.pd

Parametric spectral estimation : a fast rational model approach

http://deepblue.lib.umich.edu/bitstream/2027.42/4846/5/bac2059.0001.001.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/4846/4/bac2059.0001.001.tx

A Spectral Representation Method For Continuous-Time Stochastic System Estimation Based On Analog Data Records

In this paper a novel and effective maximum likelihood type method for the estimation of physically meaningful continuous-time stochastic systems from analog data records is introduced. The method utilizes the ARMAX canonical form and block-pulse function spectral representations, through which the problem is shown to be transformed into that of estimating an induced and special-form discrete stochastic system from spectral data. The proposed method is based on a number of key structural and probabilistic properties that this discrete system is shown to possess, including stationarity, invertibility, and the bijective transformation nature of its mapping relationship with the original continuous-time system.Unlike previous schemes, the proposed method utilizes analog data without depending upon estimates of signal derivatives or prefilters, avoids errors due to direct discretizations associated with instantaneous sampling, and is characterized by a linear transformation relationship between the discrete and the original continuous-time system parameters. This leads to additional important advantages, such as the elimination of sensitivity problems associated with highly non-linear mappings, the capability of incorporating a priori system information, and reduced computational complexity. The effectiveness of the method is verified via numerical experiments with a number of stochastic systems.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/30455/1/0000081.pd

Effective structure/parameter estimation and performance evaluation.

http://deepblue.lib.umich.edu/bitstream/2027.42/4843/5/bac2058.0002.001.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/4843/4/bac2058.0002.001.tx