Estimation of Equation Coefficients of Free and Forced String Vibrations in Continuous Medium with Consideration of Dynamic Noise and Measurement Noise

Abstract

Abstract Linear hyperbolic differential equation of partial derivatives, that sets string vibration, as well as other oscillatory processes in continuous medium and electrodynamics, is also used in many areas of theoretical physics. This article considers estimation problems of equation coefficients of free and forced string vibrations with fixed ends with consideration of additive dynamic and measurement noises. Use of a finite-difference method allowed solving partial differential equations with consideration of additive dynamic and measurement noise by solving systems of linear stationary stochastic, finite-difference and algebraic equations, expressed as state-space models. State-space model representation of string vibration equation makes it possible to use Kalman filter algorithm to make accurate estimates of string vibrations’ coordinates.