methodology. The reader is directed to a series of companion papers in order to get an overview of the methodology and to view application results for several cases [25-26] . The applications and case histories presented in this paper are part of this new general procedure for autonomous modal parameter that is based upon consistent state vectors. This method is referred to as Common Statistical Subspace Autonomous Mode Identification (CSSAMI). Note that much of the background of the CSSAMI method is based upon the Unified Matrix Polynomial Algorithm (UMPA) developed by the authors and described in a number of other papers [27-29] . 2. Background: 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 [1-3]. Following that early work, there has been a continuing interest in autonomous methods [4-24] that, in most cases, have been procedures that are formulated based upon a specific modal parameter estimation algorithm like the Eigensystem Realization Algorithm (ERA), the Polyreference Time Domain (PTD) algorithm or more recently the Polyreference Least Squares Complex Frequency (PLSCF) algorithm or the commercial version of the PLSCF, the PolyMAX ® method. Each of these past procedures have shown some promise but have not yet been widely adopted. In many cases, the procedure focussed on a single modal parameter estimation algorithm and did not develop a general procedure. Most of the past procedural methods focussed on pole density but depended on limited modal vector data to identify correlated solutions. Currently, due to increased computational speed and larger availability of memory, procedural methods can be developed that were beyond the computational scope of available hardware only a few years ago. These methods do not require any initial thresholding of the solution sets and rely upon correlation of the vector space of thousands of potential solutions as the primary identification tool. With the addition to any modal parameter estimation algorithm of the concept of pole weighted base vector, the length, and therefore sensitivity, of the extended vectors provides an additional tool that appears to be very useful. 3. Autonomous Modal Parameter Estimation Method The autonomous modal parameter estimation method utilized in the applications and case histories in the following is a general method that can be used with any algorithm that fits within the UMPA structure. A complete description of the Unified Matrix Polynomial Algorithm (UMPA) thought process can be found in a number of references developed by the authors [27-29] . This means that this method can be applied to both low and high order methods with low or high order base vectors. This also means that most commercial algorithms could take advantage of this procedure. Note that high order matrix coefficient polynomials normally have coefficient matrices of dimension that is based upon the short dimension of the data matrix (NS ×NS). In these cases, it may be useful to solve for the complete modal vector in addition to using the extended base vector as this will extend the temporal-spatial information in the base vector so that the vector will be more sensitive to change. This characteristic is what gives this autonomous method the ability to distinguish between computational and structural modal parameters. The implementation of the autonomous modal parameter estimation for this method is briefly outlined in the following steps. For complete details, please see the associated papers [25-26]. • Develop a consistency diagram using any UMPA solution method. Since this autonomous method utilizes a pole surface density plot, having a large number of iterations in the consistency diagram (due to model order, subspace iteration, starting times, equation normalization, etc.) will be potentially advantageous. However, the larger the number of solutions (represented by symbols) in the consistency diagram, the more computation time and memory will be required. However, restricting the number of solutions using clear stabilization (consistency) methods may be counterproductive. • If the UMPA method is high order (coefficient matrices of size NS ×NS), solve for the complete length, scaled vector (function of NL for all roots, structural and computational). • Based upon the pole surface density threshold, identify all possible pole densities above some minimum value. This will be a function of the number of possible solutions represented by the consistency diagram. • Sort the remaining solutions into frequency order based upon damped natural frequency ( ωr). • Construct the 10th order, pole weighted vector (state vector) for each solution. 404
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