Autonomous Modal Parameter Estimation: Methodology

Traditionally, the estimation of modal parameters from a set of measured data has required significant experience. However, as the technology has matured, increasingly, analysis is being performed by less experienced engineers or technicians. To address this development, frequently software solutions are focusing upon either wizard-based or autonomous/semiautonomous approaches. A number of autonomic approaches to estimating modal parameters from experimental data have been proposed in the past. In this paper, this history is revewed and a technique suitable for either approach is presented. By combining traditional modal parameter estimation algorithms with a-priori decision information, the process of identifying the modal parameters (frequency, damping, mode shape, and modal scaling) can be relatively simple and automated. Examples of the efficacy of this technique are shown for both laboratory and real-world applications in a related paper. Nomenclature Ni = Number of inputs. No = Number of outputs. NS = Short dimension size. NL = Long dimension size N = Number of modal frequencies. λ r = S domain polynomial root. λ r = Complex modal frequency (rad/sec). λ r = σ r + j ω r σ r = Modal damping. ω r = Damped natural frequency. zr = Z domain polynomial root. {ψ r} = Base vector (modal vector). {φ r} = Pole weighted base vector (state vector). [Ar] = Residue matrix, mode r. [I] = Identity matrix. ti = Discrete time (sec). ω i = Discrete frequency (rad/sec). si = Generalized frequency variable. x(ti) = Response function vector (No × 1)). X(ω i) = Response function vector (No × 1)). f(ti) = Input function vector (Ni × 1)) F(ω i) = Input function vector (Ni × 1)). [h(ti)] = IRF matrix (No × Ni)). [H(ω i)] = FRF matrix (No × Ni)). [α ] = Denominator polynomial matrix coefficient. [β ] = Numerator polynomial matrix coefficient. m = Model order for denominator polynomial. n = Model order for numerator polynomial. v = Model order for base vector. r = Mode number.