Sur vey of Modal Techniques Applicable to Autonomous/Semi-Autonomous Parameter Identification

Traditionally, modal analysis has been the purview of the expert. However, as the technology has matured, analysis is increasingly being performed by less experienced engineers or technicians. To address this development, software solutions are frequently focusing upon either wizard-based or autonomous/semiautonomous approaches. In this paper, sev eral techniques applicable to either approach are presented. By combining various traditional modal parameter estimation algorithms with a-priori constraint/decision information, the process of identifying the modal parameters (frequency, damping, mode shape, and modal scaling) can be greatly simplified and/or automated. Two different methods are described and examples of the efficacy of these techniques are shown for both laboratory and real-world applications. 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 ] = Numerator polynomial matrix coefficient. [β ] = Denominator polynomial matrix coefficient. m = Model order for denominator polynomial. n = Model order for numerator polynomial. v = Model order for base vector. r = Mode number.