Allyn W. Phillips

An overview of MIMO-FRF excitation/averaging/processing techniques

The use of characterized excitation and choice of averaging techniques are fundamental to the estimation of multiple input, multiple output (MIMO) frequency response function (FRF) data. The characteristics of the excitation and averaging selected greatly influence the quality of the resulting MIMO-FRF measurements. Presented is an overview of the basic excitation methods, such as random, periodic random, pseudorandom, and burst random (random transient) as well as more advanced excitation methods, such as burst-cyclic random, slow random, MOOZ random, and periodic chirps. The application of these excitation and averaging methods is discussed relative to lightly or heavily damped systems, systems with small non-linearities, FRF models, and peak to RMS (crest factor) as well as signal-to-noise ratio (SNR) issues. Experimental examples are given to demonstrate the important issues.

Forty Years of Use and Abuse of Impact Testing: A Practical Guide to Making Good FRF Measurements

Impact testing first came into common use over 40 years ago, once the fast Fourier transform (FFT) was commercially available. Over this period of time, implementation of impact testing has evolved but some of the same problems seem to reoccur. This paper documents the practical guidelines that have evolved, along with some practical examples of what happens when the guidelines are not followed, particularly with respect to overload detection and related errors. In particular, the ADC hardware differences are noted and the distortion problem associated with overloads is thoroughly reviewed. Other issues that are discussed include factors that affect force spectrum, impact hammer calibration, double impacting, use, application and correction for exponential windows and understanding how the time truncation causes leakage for a realistic case involving a lightly damped structural system.

Application of a generalized residual model to frequency domain modal parameter estimation

Residuals have long been used in frequency domain parameter estimation methods to model the influence of out-of-band modes but, typically, as a fixed set of no more than two or three terms. Recently, a systematic approach to the use of residual polynomials has led to the development of a generalized residual model. The use of a generalized residual model with rational fraction polynomial frequency domain parameter estimation methods allows the contribution of out-of-band modes to be included without increasing the model order and creating additional computational poles. Of particular interest is the use of the generalized residual for single-degree-of-freedom (s.d.o.f.) techniques, which generally do not consider the residual effects and suffer accordingly. With the use of generalized residuals, it becomes possible to properly account for nearby modes and also extract accurate residues with an s.d.o.f. algorithm. The development of the generalized residual polynomial model is outlined and a new s.d.o.f. frequency domain algorithm with generalized residuals is developed.

Techniques for Synthesizing FRFs from Analytical Models

Modal correlation of test and analytical data is an important step in system identification and model updating. The Frequency Response Assurance Criterion (FRAC) is one of the metrics that can be used to quantify the strength of correlation between the test and analytical degrees of freedom (DOF). To calculate FRAC for test and analytical data, frequency response functions (FRF) are required. Techniques to synthesize FRFs from finite element models are discussed in this paper. Methods to represent damping in analytical models are also presented. These techniques were applied to synthesize FRFs from a finite element model of a rectangular steel plate structure. Comparing the synthesized FRFs with the measured FRFs for the rectangular plate structure aided in calibrating the rectangular plate FE model. The techniques presented in this paper can be used to visually check if the test and analytical data are well correlated and for calculating FRAC metric to quantify the strength of correlation.

Requirements for a Long-term Viable, Archive Data Format

Within the vibration technical community, there is a demand for a long-term viable, open definition file format for the archiving of data and results (not to be confused with a database management structure). For many years, the Universal File Format has been the defacto standard in this area. However, as technology has progressed, the aging nature of this FORTRAN card image based format has become problematic. In order to satisfy the increasing legal requirement of long term record keeping, a flexible archive, not dependent upon any particular hardware or operating system environment, is needed. With a discussion of some of the strengths and weaknesses of existing data formats, this paper focuses upon the identified feature set needed for realistic, longterm reliable recovery of information and successful community adoption.

Application of Principal Component Analysis Methods to Experimental Structural Dynamics

Principal Component Analysis (PCA) methods have been variously developed and applied within the experimental modal community for some time based upon the underlying linear/superposition nature of structural dynamics. While historically the use of these techniques has been restricted to the areas of model order determination (Complex Mode Indicator Function [CMIF]), enhanced frequency response function estimation, and parameter identification, increasingly they are being applied to the areas of test/model validation, experimental model correlation/repeatability and experimental/structural model comparison. With the increasing volume of data being collected today, techniques which provide effective extraction of the significant data features for quick, easy comparison are essential. This paper explores the general development and application of PCA to experimental modal analysis and its ability to provide the analyst with an effective global trend visualization tool. As examples, the results from a laboratory test structure (circular plate), a civil infrastructure (bridge), and a comparative study (automotive) are presented.

Application of Modal Scaling to the Pole Selection Phase of Parameter Estimation

Modern modal parameter estimation algorithms are frequently presented as two stage solution processes where the first stage identifies the system poles and unscaled modal vectors (participation factors) of either long or short dimension, and where the second stage identifies the scaled modal vectors (residue vectors) of generally long dimension and modal scaling. This paper explores the value of having the long dimension, scaled modal information available during the pole selection process. Among the advantages of this approach is the availability of the full length residue vector for visualization and the modal scaling in order to evaluate relative contribution and physical significance. A comparison of the residue quality for this solution approach and the dominant traditional approaches is presented. The methods and results are compared using mean phase (MP), mean phase deviation (MPD), and vector scatter plots.

Development of a Long Term Viable Dynamic Data Archive Format

For nearly forty years, the Universal File Format has served as a de facto standard for cross platform data interchange and archiving. However, as technology has progressed, the aging nature of this eighty character ASCII FORTRAN card image based format has become problematic. As a result, with the ever increasing legal requirements of long term record keeping, a flexible, open definition file format suitable for viable long term archiving of data and results, which is not dependent upon any particular hardware or operating system environment has become necessary. This paper focuses upon the various (sometimes conflicting) issues involved in the decision process and the resulting principal identified features necessary for realistic, long term reliable recovery of information and successful community adoption.

Spatial Information in Autonomous Modal Parameter Estimation

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. While autonomous modal parameter estimation means slightly different things to different researchers and practitioners, for the purpose of this discussion, autonomous will require an automated procedure which sorts and processes a large number of possible modal parameter solutions to yield one consistent estimate with no user interaction after initial thresholds are chosen. In the work discussed, this final, consistent set of modal parameters is identifiable due to the combination of temporal and spatial information in a domain state vector of relatively high order (5–10). Since this domain state vector has both complex modal frequency and modal vector information as embedded content, sorting consistent estimates from the multitude of possible solutions is relatively trivial. Because this domain state vector can be developed from the results of any modal parameter estimation method, possible solutions from different traditional methods can be utilized in the autonomous procedure to yield one consistent set of modal parameters.

Support Systems for Developing System Models

From a system modeling perspective, it is important to develop an accurate mathematical model of a structure. Such a model can be built with measured frequency response functions obtained from a modal test. The test structure can be subjected to free, constrained or operating boundary conditions. Setting up a structure with either constrained or operating boundary conditions is impractical/prohibitive. It is easier to approach free boundary condition in the lab using soft supports, such as foam, shock cords, air suspension, etc. A good support system should have the least intrusion. It should not introduce nonlinearity or damping. The effectiveness of a good support system is quantified by the extent of separation of the rigid body modes from the elastic modes and a high degree of uncoupling of the dynamics of support system and the structural modes. The influence of various boundary conditions and soft support systems chosen for modeling a lightweight structures, such as Formula SAE racecar space frame, a rectangular steel plate structure and a circular aluminum plate are discussed.