2 R.J. Allemang and A.W. Phillips 1.1 Introduction The desire to estimate modal parameters automatically, once a set or multiple sets of test data are acquired, has been a subject of great interest for more than 40 years. Even in the 1960s, when modal testing was limited to analog test methods, several researchers were exploring the idea of an automated test procedure for determining modal parameters [1–3]. Today, with the increased memory and compute power of current computers used to process test data, an automated or autonomous, modal parameter estimation procedure is entirely possible and is being evaluated by numerous researchers and users. Before proceeding with a discussion of how multiple modal parameter estimation algorithms can be combined into autonomous modal parameter estimation, some discussion of the current autonomous modal parameter estimation procedure is required. In general, autonomous modal parameter estimation refers to an automated procedure that is applied to a modal parameter estimation algorithm so that no user interaction is required once the process is initiated. This typically involves setting a number of parameters or thresholds that are used to guide the process in order to exclude solutions that are not acceptable to the user. When the procedure finishes, a set of modal parameters is identified that can then be reduced or expanded if necessary. The goal is that no further reduction, expansion or interaction with the process will be required. For the purposes of further discussion, the autonomous modal parameter estimation procedure is simply an efficient mechanism for sorting a very large number of solutions into a final set of solutions that satisfies a set of criteria and thresholds that are acceptable to the user. When multiple modal parameter estimation algorithms are combined into a single autonomous procedure, this yields more estimates of the modal parameters which contribute to a statistically more significant result. Currently, the user of autonomous modal parameter estimation is assumed to be very experienced and is using autonomous modal parameter estimation as a sophisticated tool to highlight the most likely solutions based upon statistics. The experienced user will realize that the final solutions may include unrealistic solutions or non-optimal solutions and further evaluation will be required. 1.2 Background In order to discuss the impact and use of multiple modal parameter estimation algorithms in autonomous modal parameter estimation, the importance of spatial information to the solution procedure is critical. Therefore, some background is needed to clarify terminology and methodology. This background has been provided in previous papers [4–7] and will only be highlighted here in terms of spatial information, modal parameter estimation and autonomous modal parameter estimation. 1.2.1 Spatial Information Spatial information, with respect to experimental modal parameter estimation, refers to the vector information and dimension associated with the inputs and outputs of the experimental test. Essentially, this represents the locations of the sensors in the experimental test. It is important to recognize that an experimental test should always include multiple inputs and outputs in order to clearly estimate different modal vectors and to resolve modal vectors when the complex natural frequencies are close, what is called repeated or pseudo-repeated roots. Since the data matrix, normally involving frequency response functions (FRF) or impulse response functions (IRF), is considered to be symmetric or reciprocal, the data matrix can be transposed, switching the effective meaning of the row and column index with respect to the physical inputs and outputs. ŒH.!i/ No Ni DŒH.!i/ T N i No (1.1) Since many modal parameter estimation algorithms are developed on the basis of either the number of inputs (Ni) or the number of outputs (No), assuming that one or the other is larger based upon test method, some nomenclature conventions are required for ease of further discussion. In terms of the modal parameter estimation algorithms, it is more important to recognize whether the algorithm develops the solution on the basis of the larger (NL) ofNi orNo, or the smaller (NS ) ofNi or No, dimension of the experimental data. For this reason, the terminology of long (larger of Ni or No) dimension or short (smaller of Ni orNo) dimension is easier to understand without confusion.
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