Technical Notes Single-Sensor Identification of Spinning Mode Noise from Aircraft Engine

Nomenclature A, C = constant matrices in linear time-invariant system a, b = any integers B = number of blades C0 = speed of sound, m=s c = acoustic perturbation amplitude f = frequency, Hz i = complex part Jm = mth Bessel function of the first kind K = gain of Kalman filter k = spinning mode frequency, Hz ka = axial wave number, 1=m kr = radial wave number, 1=m Mj = duct-flow Mach number N = number of microphones in an array nx = number of states O = observability matrix P = estimate covariance p = flow pressure, Pa t = time, s u, v, w = velocity, m=s V = the number of stator vanes v = measurement noise with covariance R w = modeling noise with covariance Q wt = @w=@t x, r, = cylindrical coordinates x0, R = axial and radial positions of sensors x = system states y = system outputs K = circumferential position of Kth microphone, rad = flow density, kg=m