A dynamical identification method based on conditioned observations for a sound insulation system with the order determined by a new criterion index

Abstract

This paper describes a new approach to the identification of arbitrary sound insulation systems with random excitations, for practical situations in which the observations of input and transmitted (output) signals are strongly contaminated by external additive noise in the reception and transmission rooms. First, the sound insulation system is modelled by a time series representation of the relationship among the output, signal input and contaminating noise acoustic powers, with discrete time sampling, rather than by using the usual respective spectral densities in the frequency domain. An hypothetical pre-experiment with a test input of white noise is analyzed to determine the order of this time series model. From the results of this analysis, it is shown that a criterion function can be found for use in actual observations when both an arbitrary input signal and an arbitrary contaminating noise are present, and that by using this function the time series model order can be determined from the actually observed data, so that in practice such a pre-experiment is not necessary. Second, the system model parameters are successively estimated by a wide sense digital filter based on Bayes' theorem with input level conditioning. Third, these estimated parameters are then used to predict the probability distribution of the output power fluctuations for the system under arbitrary random excitations. Finally, the effectiveness of the proposed identification method is experimentally confirmed by applying it to a number of actual sound insulation systems.