Determining the Accuracy of Modal Parameter Estimation Methods

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 estimation (curve fitting) method to determine the structure’s modal properties from the FRF measurements. The curve fitting method typically “fits” an analytical model to the FRF data, (or its equivalent Impulse Response data) and estimates of the unknown modal parameters of the model are determined by this process. These parameter estimates are then assumed to be the correct modal parameters of the structure. In this paper, a number of “standard test cases” of synthesized FRFs are presented for testing modal parameter estimation methods. Twelve different FRFs are presented, that are synthesized using the parameters for three modes. Frequency spacings between the modes and modal damping values are varied to make up the different cases, which range from light modal coupling (or modal density) to very heavy coupling. Random noise is also added to the synthesized FRFs to simulate noisy measurements, giving a total of twenty-four different test cases. The advantage of this approach to curve fitter testing is, of course, that the right answers (the modal parameters used to synthesize the FRFs) are known, and can therefore be used as the basis for determining the accuracy of the fitter. Two different curve fitting methods, an SDOF (single mode-at-a-time) and an MDOF (multiple modes-at-a-time) rational fraction polynomial fitter, were tried on the test case FRFs, and the results are presented. In publishing these “standard test cases” the authors hope to encourage the adoption of a suite of published test cases by the modal testing community which could then be used to qualify the accuracy of commercially available modal testing software.